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

 

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