Quantum Mechanics for Engineers

 

Leon van Dommelen

08/26/18 Version 5.63 alpha

Copy­right and Dis­claimer

Copy­right © 2004, 2007, 2008, 2010, 2011, and on, Leon van Dom­me­len. You are al­lowed to copy and/or print out this work for your per­sonal use. How­ever, do not dis­trib­ute any parts of this work to oth­ers or post it pub­licly with­out writ­ten per­mis­sion of the au­thor. In­stead please link to this work. I want to be able to cor­rect er­rors and im­prove ex­pla­na­tions and ac­tu­ally have them cor­rected and im­proved. Every at­tempt is made to make links as per­ma­nent as pos­si­ble.

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• Ded­i­ca­tion
• Con­tents
• List of Fig­ures
• List of Ta­bles
• Pref­ace
  • To the Stu­dent
  • Ac­knowl­edg­ments
  • Com­ments and Feed­back
  
  
• I. Spe­cial Rel­a­tiv­ity
  • 1. Spe­cial Rel­a­tiv­ity [Draft]
    • 1.1 Overview of Rel­a­tiv­ity
      • 1.1.1 A note on the his­tory of the the­ory
      • 1.1.2 The mass-en­ergy re­la­tion
      • 1.1.3 The uni­ver­sal speed of light
      • 1.1.4 Dis­agree­ments about space and time
    • 1.2 The Lorentz Trans­for­ma­tion
      • 1.2.1 The trans­for­ma­tion for­mu­lae
      • 1.2.2 Proper time and dis­tance
      • 1.2.3 Sub­lu­mi­nal and su­per­lu­mi­nal ef­fects
      • 1.2.4 Four-vec­tors
      • 1.2.5 In­dex no­ta­tion
      • 1.2.6 Group prop­erty
    • 1.3 Rel­a­tivis­tic Me­chan­ics
      • 1.3.1 In­tro to rel­a­tivis­tic me­chan­ics
      • 1.3.2 La­grangian me­chan­ics
  
  
• II. Ba­sic Quan­tum Me­chan­ics
  • 2. Math­e­mat­i­cal Pre­req­ui­sites
    • 2.1 Com­plex Num­bers
    • 2.2 Func­tions as Vec­tors
    • 2.3 The Dot, oops, IN­NER Prod­uct
    • 2.4 Op­er­a­tors
    • 2.5 Eigen­value Prob­lems
    • 2.6 Her­mit­ian Op­er­a­tors
    • 2.7 Ad­di­tional Points
      • 2.7.1 Dirac no­ta­tion
      • 2.7.2 Ad­di­tional in­de­pen­dent vari­ables
  • 3. Ba­sic Ideas of Quan­tum Me­chan­ics
    • 3.1 The Re­vised Pic­ture of Na­ture
    • 3.2 The Heisen­berg Un­cer­tainty Prin­ci­ple
    • 3.3 The Op­er­a­tors of Quan­tum Me­chan­ics
    • 3.4 The Or­tho­dox Sta­tis­ti­cal In­ter­pre­ta­tion
      • 3.4.1 Only eigen­val­ues
      • 3.4.2 Sta­tis­ti­cal se­lec­tion
    • 3.5 A Par­ti­cle Con­fined In­side a Pipe
      • 3.5.1 The phys­i­cal sys­tem
      • 3.5.2 Math­e­mat­i­cal no­ta­tions
      • 3.5.3 The Hamil­ton­ian
      • 3.5.4 The Hamil­ton­ian eigen­value prob­lem
      • 3.5.5 All so­lu­tions of the eigen­value prob­lem
      • 3.5.6 Dis­cus­sion of the en­ergy val­ues
      • 3.5.7 Dis­cus­sion of the eigen­func­tions
      • 3.5.8 Three-di­men­sional so­lu­tion
      • 3.5.9 Quan­tum con­fine­ment
  • 4. Sin­gle-Par­ti­cle Sys­tems
    • 4.1 The Har­monic Os­cil­la­tor
      • 4.1.1 The Hamil­ton­ian
      • 4.1.2 So­lu­tion us­ing sep­a­ra­tion of vari­ables
      • 4.1.3 Dis­cus­sion of the eigen­val­ues
      • 4.1.4 Dis­cus­sion of the eigen­func­tions
      • 4.1.5 De­gen­er­acy
      • 4.1.6 Noneigen­states
    • 4.2 An­gu­lar Mo­men­tum
      • 4.2.1 De­f­i­n­i­tion of an­gu­lar mo­men­tum
      • 4.2.2 An­gu­lar mo­men­tum in an ar­bi­trary di­rec­tion
      • 4.2.3 Square an­gu­lar mo­men­tum
      • 4.2.4 An­gu­lar mo­men­tum un­cer­tainty
    • 4.3 The Hy­dro­gen Atom
      • 4.3.1 The Hamil­ton­ian
      • 4.3.2 So­lu­tion us­ing sep­a­ra­tion of vari­ables
      • 4.3.3 Dis­cus­sion of the eigen­val­ues
      • 4.3.4 Dis­cus­sion of the eigen­func­tions
    • 4.4 Ex­pec­ta­tion Value and Stan­dard De­vi­a­tion
      • 4.4.1 Sta­tis­tics of a die
      • 4.4.2 Sta­tis­tics of quan­tum op­er­a­tors
      • 4.4.3 Sim­pli­fied ex­pres­sions
      • 4.4.4 Some ex­am­ples
    • 4.5 The Com­mu­ta­tor
      • 4.5.1 Com­mut­ing op­er­a­tors
      • 4.5.2 Non­com­mut­ing op­er­a­tors and their com­mu­ta­tor
      • 4.5.3 The Heisen­berg un­cer­tainty re­la­tion­ship
      • 4.5.4 Com­mu­ta­tor ref­er­ence
    • 4.6 The Hy­dro­gen Mol­e­c­u­lar Ion
      • 4.6.1 The Hamil­ton­ian
      • 4.6.2 En­ergy when fully dis­so­ci­ated
      • 4.6.3 En­ergy when closer to­gether
      • 4.6.4 States that share the elec­tron
      • 4.6.5 Com­par­a­tive en­er­gies of the states
      • 4.6.6 Vari­a­tional ap­prox­i­ma­tion of the ground state
      • 4.6.7 Com­par­i­son with the ex­act ground state
  • 5. Mul­ti­ple-Par­ti­cle Sys­tems
    • 5.1 Wave Func­tion for Mul­ti­ple Par­ti­cles
    • 5.2 The Hy­dro­gen Mol­e­cule
      • 5.2.1 The Hamil­ton­ian
      • 5.2.2 Ini­tial ap­prox­i­ma­tion to the low­est en­ergy state
      • 5.2.3 The prob­a­bil­ity den­sity
      • 5.2.4 States that share the elec­trons
      • 5.2.5 Vari­a­tional ap­prox­i­ma­tion of the ground state
      • 5.2.6 Com­par­i­son with the ex­act ground state
    • 5.3 Two-State Sys­tems
    • 5.4 Spin
    • 5.5 Mul­ti­ple-Par­ti­cle Sys­tems In­clud­ing Spin
      • 5.5.1 Wave func­tion for a sin­gle par­ti­cle with spin
      • 5.5.2 In­ner prod­ucts in­clud­ing spin
      • 5.5.3 Com­mu­ta­tors in­clud­ing spin
      • 5.5.4 Wave func­tion for mul­ti­ple par­ti­cles with spin
      • 5.5.5 Ex­am­ple: the hy­dro­gen mol­e­cule
      • 5.5.6 Triplet and sin­glet states
    • 5.6 Iden­ti­cal Par­ti­cles
    • 5.7 Ways to Sym­metrize the Wave Func­tion
    • 5.8 Ma­trix For­mu­la­tion
    • 5.9 Heav­ier Atoms
      • 5.9.1 The Hamil­ton­ian eigen­value prob­lem
      • 5.9.2 Ap­prox­i­mate so­lu­tion us­ing sep­a­ra­tion of vari­ables
      • 5.9.3 Hy­dro­gen and he­lium
      • 5.9.4 Lithium to neon
      • 5.9.5 Sodium to ar­gon
      • 5.9.6 Potas­sium to kryp­ton
      • 5.9.7 Full pe­ri­odic ta­ble
    • 5.10 Pauli Re­pul­sion
    • 5.11 Chem­i­cal Bonds
      • 5.11.1 Co­va­lent sigma bonds
      • 5.11.2 Co­va­lent pi bonds
      • 5.11.3 Po­lar co­va­lent bonds and hy­dro­gen bonds
      • 5.11.4 Pro­mo­tion and hy­bridiza­tion
      • 5.11.5 Ionic bonds
      • 5.11.6 Lim­i­ta­tions of va­lence bond the­ory
  • 6. Macro­scopic Sys­tems
    • 6.1 In­tro to Par­ti­cles in a Box
    • 6.2 The Sin­gle-Par­ti­cle States
    • 6.3 Den­sity of States
    • 6.4 Ground State of a Sys­tem of Bosons
    • 6.5 About Tem­per­a­ture
    • 6.6 Bose-Ein­stein Con­den­sa­tion
      • 6.6.1 Rough ex­pla­na­tion of the con­den­sa­tion
    • 6.7 Bose-Ein­stein Dis­tri­b­u­tion
    • 6.8 Black­body Ra­di­a­tion
    • 6.9 Ground State of a Sys­tem of Elec­trons
    • 6.10 Fermi En­ergy of the Free-Elec­tron Gas
    • 6.11 De­gen­er­acy Pres­sure
    • 6.12 Con­fine­ment and the DOS
    • 6.13 Fermi-Dirac Dis­tri­b­u­tion
    • 6.14 Maxwell-Boltz­mann Dis­tri­b­u­tion
    • 6.15 Thermionic Emis­sion
    • 6.16 Chem­i­cal Po­ten­tial and Dif­fu­sion
    • 6.17 In­tro to the Pe­ri­odic Box
    • 6.18 Pe­ri­odic Sin­gle-Par­ti­cle States
    • 6.19 DOS for a Pe­ri­odic Box
    • 6.20 In­tro to Elec­tri­cal Con­duc­tion
    • 6.21 In­tro to Band Struc­ture
      • 6.21.1 Met­als and in­su­la­tors
      • 6.21.2 Typ­i­cal met­als and in­su­la­tors
      • 6.21.3 Semi­con­duc­tors
      • 6.21.4 Semi­met­als
      • 6.21.5 Elec­tronic heat con­duc­tion
      • 6.21.6 Ionic con­duc­tiv­ity
    • 6.22 Elec­trons in Crys­tals
      • 6.22.1 Bloch waves
      • 6.22.2 Ex­am­ple spec­tra
      • 6.22.3 Ef­fec­tive mass
      • 6.22.4 Crys­tal mo­men­tum
      • 6.22.5 Three-di­men­sional crys­tals
    • 6.23 Semi­con­duc­tors
    • 6.24 The P-N Junc­tion
    • 6.25 The Tran­sis­tor
    • 6.26 Zener and Avalanche Diodes
    • 6.27 Op­ti­cal Ap­pli­ca­tions
      • 6.27.1 Atomic spec­tra
      • 6.27.2 Spec­tra of solids
      • 6.27.3 Band gap ef­fects
      • 6.27.4 Ef­fects of crys­tal im­per­fec­tions
      • 6.27.5 Pho­to­con­duc­tiv­ity
      • 6.27.6 Pho­to­voltaic cells
      • 6.27.7 Light-emit­ting diodes
    • 6.28 Ther­mo­elec­tric Ap­pli­ca­tions
      • 6.28.1 Peltier ef­fect
      • 6.28.2 See­beck ef­fect
      • 6.28.3 Thom­son ef­fect
  • 7. Time Evo­lu­tion
    • 7.1 The Schrö­din­ger Equa­tion
      • 7.1.1 The equa­tion
      • 7.1.2 So­lu­tion of the equa­tion
      • 7.1.3 En­ergy con­ser­va­tion
      • 7.1.4 Sta­tion­ary states
      • 7.1.5 The adi­a­batic ap­prox­i­ma­tion
    • 7.2 Time Vari­a­tion of Ex­pec­ta­tion Val­ues
      • 7.2.1 New­ton­ian mo­tion
      • 7.2.2 En­ergy-time un­cer­tainty re­la­tion
    • 7.3 Con­ser­va­tion Laws and Sym­me­tries
    • 7.4 Con­ser­va­tion Laws in Emis­sion
      • 7.4.1 Con­ser­va­tion of en­ergy
      • 7.4.2 Com­bin­ing an­gu­lar mo­menta and par­i­ties
      • 7.4.3 Tran­si­tion types and their pho­tons
      • 7.4.4 Se­lec­tion rules
    • 7.5 Sym­met­ric Two-State Sys­tems
      • 7.5.1 A graph­i­cal ex­am­ple
      • 7.5.2 Par­ti­cle ex­change and forces
      • 7.5.3 Spon­ta­neous emis­sion
    • 7.6 Asym­met­ric Two-State Sys­tems
      • 7.6.1 Spon­ta­neous emis­sion re­vis­ited
    • 7.7 Ab­sorp­tion and Stim­u­lated Emis­sion
      • 7.7.1 The Hamil­ton­ian
      • 7.7.2 The two-state model
    • 7.8 Gen­eral In­ter­ac­tion with Ra­di­a­tion
    • 7.9 Po­si­tion and Lin­ear Mo­men­tum
      • 7.9.1 The po­si­tion eigen­func­tion
      • 7.9.2 The lin­ear mo­men­tum eigen­func­tion
    • 7.10 Wave Pack­ets
      • 7.10.1 So­lu­tion of the Schrö­din­ger equa­tion.
      • 7.10.2 Com­po­nent wave so­lu­tions
      • 7.10.3 Wave pack­ets
      • 7.10.4 Group ve­loc­ity
      • 7.10.5 Elec­tron mo­tion through crys­tals
    • 7.11 Al­most Clas­si­cal Mo­tion
      • 7.11.1 Mo­tion through free space
      • 7.11.2 Ac­cel­er­ated mo­tion
      • 7.11.3 De­cel­er­ated mo­tion
      • 7.11.4 The har­monic os­cil­la­tor
    • 7.12 Scat­ter­ing
      • 7.12.1 Par­tial re­flec­tion
      • 7.12.2 Tun­nel­ing
    • 7.13 Re­flec­tion and Trans­mis­sion Co­ef­fi­cients
  • 8. The Mean­ing of Quan­tum Me­chan­ics
    • 8.1 Schrö­din­ger’s Cat
    • 8.2 In­stan­ta­neous In­ter­ac­tions
    • 8.3 Global Sym­metriza­tion
    • 8.4 A story by Wheeler
    • 8.5 Fail­ure of the Schrö­din­ger Equa­tion?
    • 8.6 The Many-Worlds In­ter­pre­ta­tion
    • 8.7 The Ar­row of Time
  
  
• III. Gate­way Top­ics
  • 9. Nu­mer­i­cal Pro­ce­dures
    • 9.1 The Vari­a­tional Method
      • 9.1.1 Ba­sic vari­a­tional state­ment
      • 9.1.2 Dif­fer­en­tial form of the state­ment
      • 9.1.3 Us­ing La­grangian mul­ti­pli­ers
    • 9.2 The Born-Op­pen­heimer Ap­prox­i­ma­tion
      • 9.2.1 The Hamil­ton­ian
      • 9.2.2 Ba­sic Born-Op­pen­heimer ap­prox­i­ma­tion
      • 9.2.3 Go­ing one bet­ter
    • 9.3 The Hartree-Fock Ap­prox­i­ma­tion
      • 9.3.1 Wave func­tion ap­prox­i­ma­tion
      • 9.3.2 The Hamil­ton­ian
      • 9.3.3 The ex­pec­ta­tion value of en­ergy
      • 9.3.4 The canon­i­cal Hartree-Fock equa­tions
      • 9.3.5 Ad­di­tional points
  • 10. Solids
    • 10.1 Mol­e­c­u­lar Solids
    • 10.2 Ionic Solids
    • 10.3 Met­als
      • 10.3.1 Lithium
      • 10.3.2 One-di­men­sional crys­tals
      • 10.3.3 Wave func­tions of one-di­men­sional crys­tals
      • 10.3.4 Analy­sis of the wave func­tions
      • 10.3.5 Flo­quet (Bloch) the­ory
      • 10.3.6 Fourier analy­sis
      • 10.3.7 The rec­i­p­ro­cal lat­tice
      • 10.3.8 The en­ergy lev­els
      • 10.3.9 Merg­ing and split­ting bands
      • 10.3.10 Three-di­men­sional met­als
    • 10.4 Co­va­lent Ma­te­ri­als
    • 10.5 Free-Elec­tron Gas
      • 10.5.1 Lat­tice for the free elec­trons
      • 10.5.2 Oc­cu­pied states and Bril­louin zones
    • 10.6 Nearly-Free Elec­trons
      • 10.6.1 En­ergy changes due to a weak lat­tice po­ten­tial
      • 10.6.2 Dis­cus­sion of the en­ergy changes
    • 10.7 Ad­di­tional Points
      • 10.7.1 About fer­ro­mag­net­ism
      • 10.7.2 X-ray dif­frac­tion
  • 11. Ba­sic and Quan­tum Ther­mo­dy­nam­ics
    • 11.1 Tem­per­a­ture
    • 11.2 Sin­gle-Par­ti­cle ver­sus Sys­tem States
    • 11.3 How Many Sys­tem Eigen­func­tions?
    • 11.4 Par­ti­cle-En­ergy Dis­tri­b­u­tion Func­tions
    • 11.5 The Canon­i­cal Prob­a­bil­ity Dis­tri­b­u­tion
    • 11.6 Low Tem­per­a­ture Be­hav­ior
    • 11.7 The Ba­sic Ther­mo­dy­namic Vari­ables
    • 11.8 In­tro to the Sec­ond Law
    • 11.9 The Re­versible Ideal
    • 11.10 En­tropy
    • 11.11 The Big Lie of Dis­tin­guish­able Par­ti­cles
    • 11.12 The New Vari­ables
    • 11.13 Mi­cro­scopic Mean­ing of the Vari­ables
    • 11.14 Ap­pli­ca­tion to Par­ti­cles in a Box
      • 11.14.1 Bose-Ein­stein con­den­sa­tion
      • 11.14.2 Fermi­ons at low tem­per­a­tures
      • 11.14.3 A gen­er­al­ized ideal gas law
      • 11.14.4 The ideal gas
      • 11.14.5 Black­body ra­di­a­tion
      • 11.14.6 The De­bye model
    • 11.15 Spe­cific Heats
  • 12. An­gu­lar mo­men­tum
    • 12.1 In­tro­duc­tion
    • 12.2 The fun­da­men­tal com­mu­ta­tion re­la­tions
    • 12.3 Lad­ders
    • 12.4 Pos­si­ble val­ues of an­gu­lar mo­men­tum
    • 12.5 A warn­ing about an­gu­lar mo­men­tum
    • 12.6 Triplet and sin­glet states
    • 12.7 Cleb­sch-Gor­dan co­ef­fi­cients
    • 12.8 Some im­por­tant re­sults
    • 12.9 Mo­men­tum of par­tially filled shells
    • 12.10 Pauli spin ma­tri­ces
    • 12.11 Gen­eral spin ma­tri­ces
    • 12.12 The Rel­a­tivis­tic Dirac Equa­tion
  • 13. Elec­tro­mag­net­ism
    • 13.1 The Elec­tro­mag­netic Hamil­ton­ian
    • 13.2 Maxwell’s Equa­tions
    • 13.3 Ex­am­ple Sta­tic Elec­tro­mag­netic Fields
      • 13.3.1 Point charge at the ori­gin
      • 13.3.2 Dipoles
      • 13.3.3 Ar­bi­trary charge dis­tri­b­u­tions
      • 13.3.4 So­lu­tion of the Pois­son equa­tion
      • 13.3.5 Cur­rents
      • 13.3.6 Prin­ci­ple of the elec­tric mo­tor
    • 13.4 Par­ti­cles in Mag­netic Fields
    • 13.5 Stern-Ger­lach Ap­pa­ra­tus
    • 13.6 Nu­clear Mag­netic Res­o­nance
      • 13.6.1 De­scrip­tion of the method
      • 13.6.2 The Hamil­ton­ian
      • 13.6.3 The un­per­turbed sys­tem
      • 13.6.4 Ef­fect of the per­tur­ba­tion
  • 14. Nu­clei [Un­fin­ished Draft]
    • 14.1 Fun­da­men­tal Con­cepts
    • 14.2 Draft: The Sim­plest Nu­clei
      • 14.2.1 Draft: The pro­ton
      • 14.2.2 Draft: The neu­tron
      • 14.2.3 Draft: The deuteron
      • 14.2.4 Draft: Prop­erty sum­mary
    • 14.3 Draft: Overview of Nu­clei
    • 14.4 Draft: Magic num­bers
    • 14.5 Draft: Ra­dioac­tiv­ity
      • 14.5.1 Draft: Half-life and de­cay rate
      • 14.5.2 Draft: More than one de­cay process
      • 14.5.3 Draft: Other de­f­i­n­i­tions
    • 14.6 Draft: Mass and en­ergy
    • 14.7 Draft: Bind­ing en­ergy
    • 14.8 Draft: Nu­cleon sep­a­ra­tion en­er­gies
    • 14.9 Draft: Mod­el­ing the Deuteron
    • 14.10 Draft: Liq­uid drop model
      • 14.10.1 Draft: Nu­clear ra­dius
      • 14.10.2 Draft: von Weizsäcker for­mula
      • 14.10.3 Draft: Ex­pla­na­tion of the for­mula
      • 14.10.4 Draft: Ac­cu­racy of the for­mula
    • 14.11 Draft: Al­pha De­cay
      • 14.11.1 Draft: De­cay mech­a­nism
      • 14.11.2 Draft: Com­par­i­son with data
      • 14.11.3 Draft: For­bid­den de­cays
      • 14.11.4 Draft: Why al­pha de­cay?
    • 14.12 Draft: Shell model
      • 14.12.1 Draft: Av­er­age po­ten­tial
      • 14.12.2 Draft: Spin-or­bit in­ter­ac­tion
      • 14.12.3 Draft: Ex­am­ple oc­cu­pa­tion lev­els
      • 14.12.4 Draft: Shell model with pair­ing
      • 14.12.5 Draft: Con­fig­u­ra­tion mix­ing
      • 14.12.6 Draft: Shell model fail­ures
    • 14.13 Draft: Col­lec­tive Struc­ture
      • 14.13.1 Draft: Clas­si­cal liq­uid drop
      • 14.13.2 Draft: Nu­clear vi­bra­tions
      • 14.13.3 Draft: Non­spher­i­cal nu­clei
      • 14.13.4 Draft: Ro­ta­tional bands
    • 14.14 Draft: Fis­sion
      • 14.14.1 Draft: Ba­sic con­cepts
      • 14.14.2 Draft: Some ba­sic fea­tures
    • 14.15 Draft: Spin Data
      • 14.15.1 Draft: Even-even nu­clei
      • 14.15.2 Draft: Odd mass num­ber nu­clei
      • 14.15.3 Draft: Odd-odd nu­clei
    • 14.16 Draft: Par­ity Data
      • 14.16.1 Draft: Even-even nu­clei
      • 14.16.2 Draft: Odd mass num­ber nu­clei
      • 14.16.3 Draft: Odd-odd nu­clei
      • 14.16.4 Draft: Par­ity Sum­mary
    • 14.17 Draft: Elec­tro­mag­netic Mo­ments
      • 14.17.1 Draft: Clas­si­cal de­scrip­tion
      • 14.17.2 Draft: Quan­tum de­scrip­tion
      • 14.17.3 Draft: Mag­netic mo­ment data
      • 14.17.4 Draft: Quadru­pole mo­ment data
    • 14.18 Draft: Isospin
      • 14.18.1 Draft: Ba­sic ideas
      • 14.18.2 Draft: Heav­ier nu­clei
      • 14.18.3 Draft: Ad­di­tional points
      • 14.18.4 Draft: Why does this work?
    • 14.19 Draft: Beta de­cay
      • 14.19.1 Draft: In­tro­duc­tion
      • 14.19.2 Draft: En­er­get­ics Data
      • 14.19.3 Draft: Beta de­cay and magic num­bers
      • 14.19.4 Draft: Von Weizsäcker ap­prox­i­ma­tion
      • 14.19.5 Draft: Ki­netic En­er­gies
      • 14.19.6 Draft: For­bid­den de­cays
      • 14.19.7 Draft: Data and Fermi the­ory
      • 14.19.8 Draft: Par­ity vi­o­la­tion
    • 14.20 Draft: Gamma De­cay
      • 14.20.1 Draft: En­er­get­ics
      • 14.20.2 Draft: For­bid­den de­cays
      • 14.20.3 Draft: Iso­mers
      • 14.20.4 Draft: Weis­skopf es­ti­mates
      • 14.20.5 Draft: Com­par­i­son with data
      • 14.20.6 Draft: In­ter­nal con­ver­sion
  
  
• IV. Sup­ple­men­tary In­for­ma­tion
  • A. Ad­denda
    • A.1 Clas­si­cal La­grangian me­chan­ics
      • A.1.1 In­tro­duc­tion
      • A.1.2 Gen­er­al­ized co­or­di­nates
      • A.1.3 La­grangian equa­tions of mo­tion
      • A.1.4 Hamil­ton­ian dy­nam­ics
      • A.1.5 Fields
    • A.2 An ex­am­ple of vari­a­tional cal­cu­lus
    • A.3 Galilean trans­for­ma­tion
    • A.4 More on in­dex no­ta­tion
    • A.5 The re­duced mass
    • A.6 Con­stant spher­i­cal po­ten­tials
      • A.6.1 The eigen­value prob­lem
      • A.6.2 The eigen­func­tions
      • A.6.3 About free space so­lu­tions
    • A.7 Ac­cu­racy of the vari­a­tional method
    • A.8 Pos­i­tive ground state wave func­tion
    • A.9 Wave func­tion sym­me­tries
    • A.10 Spin in­ner prod­uct
    • A.11 Ther­mo­elec­tric ef­fects
      • A.11.1 Peltier and See­beck co­ef­fi­cient ball­parks
      • A.11.2 Fig­ure of merit
      • A.11.3 Phys­i­cal See­beck mech­a­nism
      • A.11.4 Full ther­mo­elec­tric equa­tions
      • A.11.5 Charge lo­ca­tions in ther­mo­electrics
      • A.11.6 Kelvin re­la­tion­ships
    • A.12 Heisen­berg pic­ture
    • A.13 In­te­gral Schrö­din­ger equa­tion
    • A.14 The Klein-Gor­don equa­tion
    • A.15 Quan­tum Field The­ory in a Nanoshell
      • A.15.1 Oc­cu­pa­tion num­bers
      • A.15.2 Cre­ation and an­ni­hi­la­tion op­er­a­tors
      • A.15.3 The ca­Her­mi­tians
      • A.15.4 Re­cast­ing a Hamil­ton­ian as a quan­tum field one
      • A.15.5 The har­monic os­cil­la­tor as a bo­son sys­tem
      • A.15.6 Canon­i­cal (sec­ond) quan­ti­za­tion
      • A.15.7 Spin as a fermion sys­tem
      • A.15.8 More sin­gle par­ti­cle states
      • A.15.9 Field op­er­a­tors
      • A.15.10 Non­rel­a­tivis­tic quan­tum field the­ory
    • A.16 The adi­a­batic the­o­rem
    • A.17 The vir­ial the­o­rem
    • A.18 The en­ergy-time un­cer­tainty re­la­tion­ship
    • A.19 Con­ser­va­tion Laws and Sym­me­tries
      • A.19.1 An ex­am­ple sym­me­try trans­for­ma­tion
      • A.19.2 Phys­i­cal de­scrip­tion of a sym­me­try
      • A.19.3 De­riva­tion of the con­ser­va­tion law
      • A.19.4 Other sym­me­tries
      • A.19.5 A gauge sym­me­try and con­ser­va­tion of charge
      • A.19.6 Reser­va­tions about time shift sym­me­try
    • A.20 An­gu­lar mo­men­tum of vec­tor par­ti­cles
    • A.21 Pho­ton type 2 wave func­tion
      • A.21.1 The wave func­tion
      • A.21.2 Sim­pli­fy­ing the wave func­tion
      • A.21.3 Pho­ton spin
      • A.21.4 En­ergy eigen­states
      • A.21.5 Nor­mal­iza­tion of the wave func­tion
      • A.21.6 States of def­i­nite lin­ear mo­men­tum
      • A.21.7 States of def­i­nite an­gu­lar mo­men­tum
    • A.22 Forces by par­ti­cle ex­change
      • A.22.1 Clas­si­cal se­lec­to­sta­t­ics
      • A.22.2 Clas­si­cal se­lec­to­dy­nam­ics
      • A.22.3 Quan­tum se­lec­to­sta­t­ics
      • A.22.4 Poin­caré and Ein­stein try to save the uni­verse
      • A.22.5 Lorenz saves the uni­verse
      • A.22.6 Gupta-Bleuler con­di­tion
      • A.22.7 The con­ven­tional La­grangian
      • A.22.8 Quan­ti­za­tion fol­low­ing Fermi
      • A.22.9 The Coulomb po­ten­tial and the speed of light
    • A.23 Quan­ti­za­tion of ra­di­a­tion
      • A.23.1 Prop­er­ties of clas­si­cal elec­tro­mag­netic fields
      • A.23.2 Pho­ton wave func­tions
      • A.23.3 The elec­tro­mag­netic op­er­a­tors
      • A.23.4 Prop­er­ties of the ob­serv­able elec­tro­mag­netic field
    • A.24 Quan­tum spon­ta­neous emis­sion
    • A.25 Mul­ti­pole tran­si­tions
      • A.25.1 Ap­prox­i­mate Hamil­ton­ian
      • A.25.2 Ap­prox­i­mate mul­ti­pole ma­trix el­e­ments
      • A.25.3 Cor­rected mul­ti­pole ma­trix el­e­ments
      • A.25.4 Ma­trix el­e­ment ball­parks
      • A.25.5 Se­lec­tion rules
      • A.25.6 Ball­park de­cay rates
      • A.25.7 Wave func­tions of def­i­nite an­gu­lar mo­men­tum
      • A.25.8 Weis­skopf and Moszkowski es­ti­mates
      • A.25.9 Er­rors in other sources
    • A.26 Fourier in­ver­sion the­o­rem and Par­se­val
    • A.27 De­tails of the an­i­ma­tions
    • A.28 WKB The­ory of Nearly Clas­si­cal Mo­tion
    • A.29 WKB so­lu­tion near the turn­ing points
    • A.30 Three-di­men­sional scat­ter­ing
      • A.30.1 Par­tial wave analy­sis
      • A.30.2 Par­tial wave am­pli­tude
      • A.30.3 The Born ap­prox­i­ma­tion
    • A.31 The Born se­ries
    • A.32 The evo­lu­tion of prob­a­bil­ity
    • A.33 Ex­pla­na­tion of the Lon­don forces
    • A.34 Ex­pla­na­tion of Hund’s first rule
    • A.35 The third law
    • A.36 Al­ter­nate Dirac equa­tions
    • A.37 Maxwell’s wave equa­tions
    • A.38 Per­tur­ba­tion The­ory
      • A.38.1 Ba­sic per­tur­ba­tion the­ory
      • A.38.2 Ion­iza­tion en­ergy of he­lium
      • A.38.3 De­gen­er­ate per­tur­ba­tion the­ory
      • A.38.4 The Zee­man ef­fect
      • A.38.5 The Stark ef­fect
    • A.39 The rel­a­tivis­tic hy­dro­gen atom
      • A.39.1 In­tro­duc­tion
      • A.39.2 Fine struc­ture
      • A.39.3 Weak and in­ter­me­di­ate Zee­man ef­fect
      • A.39.4 Lamb shift
      • A.39.5 Hy­per­fine split­ting
    • A.40 Deuteron wave func­tion
    • A.41 Deuteron model
      • A.41.1 The model
      • A.41.2 The re­pul­sive core
      • A.41.3 Spin de­pen­dence
      • A.41.4 Non­cen­tral force
      • A.41.5 Spin-or­bit in­ter­ac­tion
    • A.42 Nu­clear forces
      • A.42.1 Ba­sic Yukawa po­ten­tial
      • A.42.2 OPEP po­ten­tial
      • A.42.3 Ex­pla­na­tion of the OPEP po­ten­tial
      • A.42.4 Mul­ti­ple pion ex­change and such
    • A.43 Clas­si­cal vi­brat­ing drop
      • A.43.1 Ba­sic de­f­i­n­i­tions
      • A.43.2 Ki­netic en­ergy
      • A.43.3 En­ergy due to sur­face ten­sion
      • A.43.4 En­ergy due to Coulomb re­pul­sion
      • A.43.5 Fre­quency of vi­bra­tion
    • A.44 Rel­a­tivis­tic neu­tri­nos
    • A.45 Fermi the­ory
      • A.45.1 Form of the wave func­tion
      • A.45.2 Source of the de­cay
      • A.45.3 Al­lowed or for­bid­den
      • A.45.4 The nu­clear op­er­a­tor
      • A.45.5 Fermi’s golden rule
      • A.45.6 Mop­ping up
      • A.45.7 Elec­tron cap­ture
  • D. De­riva­tions
    • D.1 Generic vec­tor iden­ti­ties
    • D.2 Some Green’s func­tions
      • D.2.1 The Pois­son equa­tion
      • D.2.2 The screened Pois­son equa­tion
    • D.3 La­grangian me­chan­ics
      • D.3.1 La­grangian equa­tions of mo­tion
      • D.3.2 Hamil­ton­ian dy­nam­ics
      • D.3.3 Fields
    • D.4 Lorentz trans­for­ma­tion de­riva­tion
    • D.5 Lorentz group prop­erty de­riva­tion
    • D.6 Lorentz force de­riva­tion
    • D.7 De­riva­tion of the Euler for­mula
    • D.8 Com­plete­ness of Fourier modes
    • D.9 Mo­men­tum op­er­a­tors are Her­mit­ian
    • D.10 The curl is Her­mit­ian
    • D.11 Ex­ten­sion to three-di­men­sional so­lu­tions
    • D.12 The har­monic os­cil­la­tor so­lu­tion
    • D.13 The har­monic os­cil­la­tor and un­cer­tainty
    • D.14 The spher­i­cal har­mon­ics
      • D.14.1 De­riva­tion from the eigen­value prob­lem
      • D.14.2 Par­ity
      • D.14.3 So­lu­tions of the Laplace equa­tion
      • D.14.4 Or­thog­o­nal in­te­grals
      • D.14.5 An­other way to find the spher­i­cal har­mon­ics
      • D.14.6 Still an­other way to find them
    • D.15 The hy­dro­gen ra­dial wave func­tions
    • D.16 Con­stant spher­i­cal po­ten­tials de­riva­tions
      • D.16.1 The eigen­func­tions
      • D.16.2 The Rayleigh for­mula
    • D.17 In­ner prod­uct for the ex­pec­ta­tion value
    • D.18 Eigen­func­tions of com­mut­ing op­er­a­tors
    • D.19 The gen­er­al­ized un­cer­tainty re­la­tion­ship
    • D.20 De­riva­tion of the com­mu­ta­tor rules
    • D.21 So­lu­tion of the hy­dro­gen mol­e­c­u­lar ion
    • D.22 Unique ground state wave func­tion
    • D.23 So­lu­tion of the hy­dro­gen mol­e­cule
    • D.24 Hy­dro­gen mol­e­cule ground state and spin
    • D.25 Num­ber of bo­son states
    • D.26 Den­sity of states
    • D.27 Ra­di­a­tion from a hole
    • D.28 Kirch­hoff’s law
    • D.29 The thermionic emis­sion equa­tion
    • D.30 Num­ber of con­duc­tion band elec­trons
    • D.31 In­te­gral Schrö­din­ger equa­tion
    • D.32 In­te­gral con­ser­va­tion laws
    • D.33 Quan­tum field de­riva­tions
    • D.34 The adi­a­batic the­o­rem
    • D.35 The evo­lu­tion of ex­pec­ta­tion val­ues
    • D.36 Pho­ton wave func­tion de­riva­tions
      • D.36.1 Rewrit­ing the en­ergy in­te­gral
      • D.36.2 An­gu­lar mo­men­tum states
    • D.37 Forces by par­ti­cle ex­change de­riva­tions
      • D.37.1 Clas­si­cal en­ergy min­i­miza­tion
      • D.37.2 Quan­tum en­ergy min­i­miza­tion
      • D.37.3 Rewrit­ing the La­grangian
      • D.37.4 Coulomb po­ten­tial en­ergy
    • D.38 Time-de­pen­dent per­tur­ba­tion the­ory
    • D.39 Se­lec­tion rules
    • D.40 Quan­ti­za­tion of ra­di­a­tion de­riva­tions
    • D.41 De­riva­tion of the Ein­stein B co­ef­fi­cients
    • D.42 De­riva­tion of the Ein­stein A co­ef­fi­cients
    • D.43 Mul­ti­pole de­riva­tions
      • D.43.1 Ma­trix el­e­ment for lin­ear mo­men­tum modes
      • D.43.2 Ma­trix el­e­ment for an­gu­lar mo­men­tum modes
      • D.43.3 Weis­skopf and Moszkowski es­ti­mates
    • D.44 De­riva­tion of group ve­loc­ity
    • D.45 Mo­tion through crys­tals
      • D.45.1 Prop­a­ga­tion speed
      • D.45.2 Mo­tion un­der an ex­ter­nal force
      • D.45.3 Free-elec­tron gas with con­stant elec­tric field
    • D.46 De­riva­tion of the WKB ap­prox­i­ma­tion
    • D.47 Born dif­fer­en­tial cross sec­tion
    • D.48 About La­grangian mul­ti­pli­ers
    • D.49 The gen­er­al­ized vari­a­tional prin­ci­ple
    • D.50 Spin de­gen­er­acy
    • D.51 Born-Op­pen­heimer nu­clear mo­tion
    • D.52 Sim­pli­fi­ca­tion of the Hartree-Fock en­ergy
    • D.53 In­te­gral con­straints
    • D.54 De­riva­tion of the Hartree-Fock equa­tions
    • D.55 Why the Fock op­er­a­tor is Her­mit­ian
    • D.56 Num­ber of sys­tem eigen­func­tions
    • D.57 The par­ti­cle en­ergy dis­tri­b­u­tions
    • D.58 The canon­i­cal prob­a­bil­ity dis­tri­b­u­tion
    • D.59 Analy­sis of the ideal gas Carnot cy­cle
    • D.60 Checks on the ex­pres­sion for en­tropy
    • D.61 Chem­i­cal po­ten­tial in the dis­tri­b­u­tions
    • D.62 Fermi-Dirac in­te­grals at low tem­per­a­ture
    • D.63 An­gu­lar mo­men­tum un­cer­tainty
    • D.64 Spher­i­cal har­mon­ics by lad­der op­er­a­tors
    • D.65 How to make Cleb­sch-Gor­dan ta­bles
    • D.66 The tri­an­gle in­equal­ity
    • D.67 Mo­men­tum of shells
    • D.68 Awk­ward ques­tions about spin
    • D.69 More awk­ward­ness about spin
    • D.70 Emer­gence of spin from rel­a­tiv­ity
    • D.71 Elec­tro­mag­netic com­mu­ta­tors
    • D.72 Var­i­ous elec­tro­sta­tic de­riva­tions.
      • D.72.1 Ex­is­tence of a po­ten­tial
      • D.72.2 The Laplace equa­tion
      • D.72.3 Egg-shaped di­pole field lines
      • D.72.4 Ideal charge di­pole delta func­tion
      • D.72.5 In­te­grals of the cur­rent den­sity
      • D.72.6 Lorentz forces on a cur­rent dis­tri­b­u­tion
      • D.72.7 Field of a cur­rent di­pole
      • D.72.8 Biot-Savart law
    • D.73 Or­bital mo­tion in a mag­netic field
    • D.74 Elec­tron spin in a mag­netic field
    • D.75 Solv­ing the NMR equa­tions
    • D.76 Har­monic os­cil­la­tor re­vis­ited
    • D.77 Im­pen­e­tra­ble spher­i­cal shell
    • D.78 Shell model quadru­pole mo­ment
    • D.79 De­riva­tion of per­tur­ba­tion the­ory
    • D.80 Hy­dro­gen ground state Stark ef­fect
    • D.81 Dirac fine struc­ture Hamil­ton­ian
    • D.82 Clas­si­cal spin-or­bit de­riva­tion
    • D.83 Ex­pec­ta­tion pow­ers of r for hy­dro­gen
    • D.84 Band gap ex­pla­na­tion de­riva­tions
  • N. Notes
    • N.1 Why this book?
    • N.2 His­tory and wish list
    • N.3 Na­ture and real eigen­val­ues
    • N.4 Are Her­mit­ian op­er­a­tors re­ally like that?
    • N.5 Why bound­ary con­di­tions are tricky
    • N.6 Is the vari­a­tional ap­prox­i­ma­tion best?
    • N.7 Shield­ing ap­prox­i­ma­tion lim­i­ta­tions
    • N.8 Why the s states have the least en­ergy
    • N.9 Ex­pla­na­tion of the band gaps
    • N.10 A less fishy story
    • N.11 Bet­ter de­scrip­tion of two-state sys­tems
    • N.12 Sec­ond quan­ti­za­tion in other books
    • N.13 Com­bin­ing an­gu­lar mo­men­tum fac­tors
    • N.14 The elec­tric mul­ti­pole prob­lem
    • N.15 A tenth of a googol in uni­verses
    • N.16 A sin­gle Slater de­ter­mi­nant is not ex­act
    • N.17 Gen­er­al­ized or­bitals
    • N.18 Cor­re­la­tion en­ergy
    • N.19 Am­bi­gu­i­ties in elec­tron affin­ity
    • N.20 Why Flo­quet the­ory should be called so
    • N.21 Su­per­flu­id­ity ver­sus BEC
    • N.22 The mech­a­nism of fer­ro­mag­net­ism
    • N.23 Fun­da­men­tal as­sump­tion of sta­tis­tics
    • N.24 A prob­lem if the en­ergy is given
    • N.25 The recipe of life
    • N.26 Physics of the fun­da­men­tal com­mu­ta­tors
    • N.27 Mag­ni­tude of com­po­nents of vec­tors
    • N.28 Adding an­gu­lar mo­men­tum com­po­nents
    • N.29 Cleb­sch-Gor­dan ta­bles are bidi­rec­tional
    • N.30 Ma­chine lan­guage Cleb­sch-Gor­dan ta­bles
    • N.31 Ex­is­tence of mag­netic monopoles
    • N.32 More on Maxwell’s third law
    • N.33 Set­ting the record straight on align­ment
    • N.34 NuDat 2 data se­lec­tion
    • N.35 Auger dis­cov­ery
    • N.36 Draft: Cage-of-Fara­day pro­posal
  
  
• Web Pages
• Ref­er­ences
• No­ta­tions
• In­dex

 

https://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/index.html 

 

 

Thermodynamics

 hermodynamics is a subject at the intersection of physics, chemistry, engineering and information technology, and that is reflected in the content in this lecture. Building on the introductory coverage of thermal physics in the Classical Physics module in Year 1, we will discuss the laws of thermodynamics and consider the irreversibility of processes and introduce entropy as a measure of it. The implications of this for heat engines (and, by extension, other engineering processes) will be discussed as well as how irreversibility determines phase equilibria via concepts such as free energy. Finally, statistical mechanics is invoked to explain the behaviour of different types of ensembles of particles, leading to distribution functions needed in other areas of physics such as Condensed Matter or Atomic and Molecular Physics, which are covered in a number of Year 3 modules.

Contents   [subject index]

1. What is Thermodynamics?
2. Heat and the Zeroth Law
3. Work and the First Law
4. Heat engines and the Second Law
5. Entropy and reversibility
6. Phase equilibria
7. Van-der-Waals gas
8. Mixtures - the chemical potential
9. Boltzmann distribution
10. Quantum statistics
11. Ensemble statistics

 

 https://users.aber.ac.uk/ruw/teach/215/

 

Lectures in Chemistry Dr. Samuel A. Abrash

 Dr. Samuel A. Abrash

 

 

 

Associate Professor
Gottwald Science Center, C208
University of Richmond, VA 23173
office phone : (804) 289-8248
home phone : (804) 323-7363
E-mail: sabrash@richmond.edu

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Courses

• Chem 110 - Pollutants in the Environment.
• Syllabus
• Tentative lecture schedule
• Chem 110 Lab
• Lab Schedule
• Policies, Safety and Notebook Requirements
• Chemical Bonds, Molecular Models, and Molecular Shapes - Lab Lecture
• Visibly Delighted:  How Do Colored Solutions Interact With Light? - Lab Lecture
• Refrigerant Gases and Pollutant Gases - Lab Lecture
• Solids in Cigarette Smoke - Lab Lecture
• Chemical Moles - Lab Lecture
• Hot Stuff - Lab Lecture
• Energy from Fuels - Lab Lecture
• Can Waste Oil Be Turned Into A Fuel - Lab Lecture
• A Conductivity Detector for Ions AND Can We Get Electricity from Chemical Reactions? - Labs Lecture
• Which Common Materials Are Acids or Bases AND Reactions of Acids With Common Substances - Labs Lecture
• Analysis of Westhampton Lake Water (Yuck!) - Lab Lecture
• Why (Actually How) Do Plastics Get Sorted for Recycling? - Lab Lecture
• Solubilities - An Investigation
• Chem 141
• Syllabus
• Lectures One Through Four
• Lectures Five Through Eight
• Lectures Nine Through Twelve
• Lectures Thirteen Through Sixteen
• Lectures Seventeen Through Twenty
• Lectures Twenty One Through Twenty Four
• Lectures Twenty Five Through Twenty Eight
• Lectures Twenty Nine Through Thirty Two
• Lectures Thirty Three Through Thirty Five
• Chem 141 Laboratory
• FAQ on Syllabus, Safety, Significant Figures, and Excel
• Lab Lecture for Spectrometric Determination of Iron Concentration
• Lab Lecture for Qualitative Analysis of Reactions
• Lab Lecture for Message in a Bottle
• Lab Lecture for Thermochemistry A: Heats of Chemical Processes
• Lab Lecture for Thermochemistry B: Salts and Society
• Lab Lecture for VSEPR/Spartan
• Lab Lecture for Exploring Buffers
• Lab Lecture for Reaction Kinetics
• Chem 309 - Physical Chemistry :
• syllabus
• Lecture Notes on State Functions, Equations of State, and Ideal and Real Gases
• Lecture Notes on Work, Heat, The First Law, State Functions, Heat Capacity, Adiabatic Processes and Thermochemistry
• Lecture Notes on Heat Engines, Entropy and the Second and Third Laws of Thermodynamics
• Lecture Notes on Thermodynamic Potentials, Maxwell Relations, The Thermodynamic Square, Thermodynamic Equations of State and Fugacity
• Lecture Notes on Phase Diagrams, The Clapeyron Equation, and First and Second Order Phase Transitions
• Lecture Notes on Mixtures, Activities, Colligative Properties and the Gibbs Phase Rule
• Lecture Notes on Chemical Equilibrium
• Lecture Notes on Electrochemical Cells, Ionic Activity and the Nernst Equation
• Lecture Notes on Chemical Kinetics
• Problem Set One (Due at the end of class, Wednesday, September 1st)
• Problem Set Two (Due at the end of class, Friday, September 10th)
• Chem 310
• The syllabus can be found on the course Blackboard Page
• Lecture notes on Experiments Leading to Quantum Mechanics and Introduction to the Schrodinger Eqn
• Lecture notes on Operators, Particle in a Box, Quantum Mechanical Averages and Multidimensional Problems
• Lecture notes on Harmonic Oscillator, Rigid Rotator, Angular Momentum and the Time Dependent Schrodinger Eqn
• Lecture notes on the Hydrogen Atom, Perturbation Theory, Introduction to the Helium Atom, and the Variational Method
• Lecture notes on The Rest of the Helium Atom, Electron Spin and the Pauli Exclusion Principle
• Lecture notes on Slater Determinants, the Hartree-Fock Approximation, Term Symbols, and Periodic Properties
• Lecture notes on the Born-Oppenheimer Approximation, the Hydrogen Molecule Ion, the Hydrogen Molecule, and the LCAO Approach to Molecular Orbitals
• Lecture notes on Molecular Electronic Configurations, Valence Bond Theory, Huckel MO Theory, Electronegativity, Ionic Bonding and Intermolecular Forces
• Lecture notes on Molecular Spectroscopy
• Environmental Studies 201: Introduction to Environmental Studies
  • syllabus
  • course schedule: please see the course blackboard page for the course schedule
  • old tests

Resources for Courses

Chem 309-310 Physical Chemistry

• C-Mor Magnetic Susceptibility Tutorial, by W. Myers and R. Kanters
• NIST Webbook

This page has in a very convenient form thermochemical data, mass spectroscopic data and infrared spectra for a large number of molecules.

 

Useful and Interesting Chemistry Links.

• WebSpectra

This site is a tool for learning how to interpret NMR and IR spectra. It consists of a library of problems in NMR and IR spectroscopy ranging in difficulty from introductory to advanced. The site also includes instructional materials and tools to assist students in learning about NMR and IR spectroscopy.

• Chemistry Index

This is an amazing chemistry site. Although it puts advertisements and items for sale first, it provides access to a large number of useful sites and programs. It includes links to 100 free chemistry databases, chemical industry www yellow pages, chemistry software, including freeware and shareware, Online Journals, Patents, Jobs, Reaction Mechanisms, Sites and Tools for Spectroscopy, Information on Chemistry Societies Worldwide, and a large index of other chemistry related websites.

• ChemFinder

This site allows you to search for a number of molecules by name, formula or CAS number. It allows searches by structure if you have ChemDraw with the appropriate plug-in. For the molecules in its data base it provides a variety of useful physical properties. (Thanks to Suzanne Vogel for bringing this to my attention.)

• Kent Wilson's Group Home Page

A very good source on undergraduate level physical and general chemistry (lots of images, videos etc.)

• Mike Colvin's Introduction to Quantum Chemistry

A good source on graduate level quantum chemistry (it's a whole book, with diagrams, images, refs etc.)

• The Molecular Modeling Group in Italy

A lot of good information, and lots of links.

• Overview of Molecular Forces in Relation to Protein Structure

Quantum Chemistry tutorials, images, very good protein-oriented site.

• Computational Chemistry and Organic Synthesis

An excellent site for information about transition states, with images.

• Molecular Simulations Inc. (Commercial Site)

The site contains some high-quality images (available in their gallery). It is especially
good for proteins and solid state materials.

• Department of Chemistry, Imperial College, UK.

This site has lots and lots of links, but more computational rather than quantum
chemical resources.

• Martin Leboeuf's page

Few but good quality images of molecules etc, and a video of an MD simulation.

• Soaring Bear's Computational Chemistry page

This site has lots of links to computational chemistry resources.

Research Projects

• Photochemistry and dynamics of weakly bound complexes in rare gas matrices; ab initio calculations of the gas phase ion-molecule reaction; photochemistry of silicon containing compounds on triplet surfaces.

Personal Information

• Curriculum Vitae

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| Faculty | Department | UR |

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CHEM 658, ADVANCED PHYSICAL CHEMISTRY

 

Dr. Carol Venanzi

Office: 323B Tiernan

(973) 596-3596

venanzi@adm.njit.edu

COURSE OBJECTIVES

 

Quantum chemistry uses high-level mathematics as a tool to understand atomic and molecular structure and properties, as well as chemical reactivity. The purpose of this course is to provide an introduction to the mathematical foundations of quantum chemistry, as well as a practical, hands-on experience with a quantum mechanics software package.

We will derive the Schrödinger Eq. for one quantum mechanical particle (electron) in one dimension. Over the next few weeks, we will learn how to solve the Schrödinger Eq. rigorously for model systems and for atoms. There will not be sufficient time to give a detailed description of the quantum mechanical treatment of molecules. However, the laboratory sessions will immediately start with techniques for calculating molecular structure and properties. There are many software programs available which one can use as a "black box" to carry out various types of quantum mechanical calculations without being an expert in the field. We will use the Spartan program from Wavefunction, Inc. The program allows graphical input of molecular structure, menu-driven input to quantum chemistry calculational programs, and graphical analysis of molecular properties. However, the difficulty lies in knowing what type of quantum mechanical model (or approximation) is appropriate for the system under study and in interpreting the results. For that reason, we will survey the semi-empirical, ab initio, and molecular mechanics techniques used by the software package to calculate molecular structure and properties. The recommended Additional Readings should help clarify the strengths and weaknesses of each of these techniques. Each student will formulate and carry out a short research project using Spartan. An important part of this exercise will be in choosing a molecular orbital technique appropriate to the project.

 

Syllabus

Lecture Notes

Additional Notes

Additional Readings

Problem Set Assignments

Problem Set Answers

How to Prepare the Project

Spartan