Atomic Movies Demonstration

How to use the animator
Run the demonstration (about 120 kBytes data) 
Run two animations in one window (about 240 kBytes data) (Best on newer machines and larger screens, minimum 800 pixels wide). If you use Microsoft Exploder, please read the tips, part about two animations in one frame. 
Explanation of the Atomic Movies 
Some tips for collision physicists 
Article by Mette Machholm and Christine Courbin who used the movies in research

Entry point of the normal presentation of Machholm's and Courbin's calculations


Authors: 
Irina Otdelnova, L. Kocbach, present setup 
Mette Machholm and Christine Courbin, Wavefunction Calculations 
Martin Holecko, The javascript animator used in the linked animations (Prague) 
Ladislav Kocbach, The present modification of Holecko's animator, and for the Atomic movies the original animator for X-windows, Mac and DOS (Bergen)

jsImagePlayer 1.0 (C) 1996 by Martin Holecko of Computer Graphics Group September 1996, PRAHA, Czech Republic  Image Player modified by L. Kocbach.

 http://www-troja.fjfi.cvut.cz/~ladi/ATCOL/demo.html

Some demonstrations of Atomic Movies based on thesis of Irina Otdelnova

• Animated wavefunctions (Mette Machholm)
• First animated GIFs by MATLAB
• Test -Animated wavefunctions by MATLAB
• 1998: New Collision Movie-Animated wavefunctions by MATLAB
• 1998: Other current part: New Collision Movie-Animated wavefunctions by MATLAB
• Testing Browser and mpeg players

Classical and quantum descriptions

NEXT: 2010_08_26 next lecture note

Classical and quantum descriptions







Reference: http://web.ift.uib.no/AMOS/PHYS261/2010_08_24/index.html

Atomic Physics and Physical Optics

Physical Optics Part PHYS261 can be found bellow


Atomic physics Part PHYS261

• 0 - Physics of atoms - Introduction - Hydrogen-like
• 1 - Helium and two electron atoms
• 2 - Many electron atoms
• 3 - Light - Atom Interaction

0. Physics of atoms - Introduction

History
Hydrogen and hydrogen-like ions
Quantum Mechanics
Textbook facts, Schrödinger Equation
Wavefunctions
Spectra, Selection rules
Rydberg atoms

1. Helium and two electron atoms

Coordinate system, Schrödinger Equation
Two electrons and spin
Helium spectra
Symmetry and Antisymmetry of wavefunctions
Parahelium and Orthohelium
Approximations to describe helium atom
Evaluation of repulsion term - Radial Integral
Exchange interaction
Variational method
Doubly excited states of Helium

2. Many electron atoms

Pauli-principle    and Hund’s rule
Antisymmetric functions for n-particles
Filling Shells
Ionization energies
Hartree Method - Selfconsistent field
Configurations
Screened potential and Centrifugal barrier
Slater Determinants
        Helium example
        Lithium example - Counting nonzero terms

Schrödinger equation from variational method
Variational method - deriving Hartree-Fock Equations
Total energy and the selfconsistent orbital energies
Evaluation of electron repulsion  
Configuration mixing

3. Light - Atom Interaction

Overview of physical phenomena involved

Time dependent QM
Quantum Theory of Electromagnetic Field
Charged Particles In an Electromagnetic Field

Time dependent QM

Two-well problem vs One level in continuum
Time-Dependent Schrödinger Equation Perturbation theory for TDSE
Dirac delta-function
Fermi Golden Rule
Density of States
Constant rate and exponential decay
Line width from exponential decay
Golden Rule Simulator Time-Dep.  Schrödinger Eq. in Simulator

Quantum Theory of Electromagnetic Field

Eigenmodes for coupled vibrations.
Algebraic Method for Harmonic Oscillator
Quantum Theory of extended systems - fields  

Charged Particles In an Electromagnetic Field 

The Hamiltonian of Interaction

Emission of Radiation by Excited Atom

The matrix element reduction
Dipole Approximation
Detailed Evaluation of Emission rate
Final W = 1 / T result ( T - lifetime )
Stimulated emission

Outline of the Course - Physical Optics part 

Study materials:
There will be distributed detailed notes during the lecture period (for both parts).
References to other books and texts will be given throughout the lectures.
It is not necessary to purchase a specific book.

Exam:
The examination is oral and will take place in the first part of December. The precise date will be agreed on,
depending on the needs of the students.

1. Maxwell’s Equations
   • Linearity and Superposition Principle
   • Phase Velocity and Group Velocity
2. Pulse Propagation in a Dispersive Medium
3. Harmonic Plane Waves - Polarisation
4. Reflection and refraction of a plane wave
5. Generalisation of the reflection law and Snell’s law
6. Reflectance and transmittance
7. Unpolarised light (natural light)
8. Rotation of the plane of polarisation upon reflection and refraction
9. Boundary Value Problems
10. Rayleigh-Sommerfeld’s and Kirchhoff’s diffraction integrals
11. Diffraction problems
    • Fresnel diffraction
    • Fraunhofer diffraction
    • Circular aperture
    • Rectangular aperture
12. Focusing and imaging
    • Aberrations
13. Electromagnetic radiation problems
    • Field radiated by a localised source
    • Field due to a point source - Green’s function
    • Field radiated by a dipole
    • Retarded solution of the wave equation
14. Asymptotic diffraction theory

to index 

Reference: http://web.ift.uib.no/AMOS/PHYS261/2012_08_21/index.html

Web-Based Quantum Mechanics Course

• Review: The Fundamental Assumptions of Quantum Mechanics

  • A free particle, one-dimensional wave packets, the Heisenberg uncertainty relations, the time evolution of a free wave packet, the spreading of a wave packet

• Review: Square Potentials

  • A particle in a time-independent scalar potential, potential steps, square wells, d-function potentials

• The WKB Approximation

  • The WKB approximations for bound states

• Mathematical Foundations of Quantum Mechanics

  • Linear vector spaces, Dirac notation, subspaces, linear operators, Hermitian operators, unitary operators, function of operators, representations in state space, change of representation, the eigenvalue problem, commuting observables, the |r> and |p> representations

• The Postulates of Quantum Mechanics

  • Postulates, mean value and root-mean-square deviation, conservation of probability, the evolution operator

• Representations

  • The Schroedinger picture, the Heisenberg picture, the interaction picture, time-dependent perturbation theory, the evolution of the mean value of an observable, interference effects

• The Density Matrix

  • A statistical mixture of states, the density operator, the physical meaning of the density matrix and the density operator

• The Harmonic Oscillator

  • The eigenvalues and eigenfunctions of the 1D harmonic oscillator, the mean value and root mean square deviation of X and P, coherent states, tensor product spaces, the 3D harmonic oscillator

• Two-Level Systems (A Spin 1/2 particle)

  • Spin, a spin 1/2 particle in a uniform magnetic field, a general study of a two-level system

• Two Spin 1/2 particles

  • The tensor product space of two spin 1/2 particles

• Angular Momentum

  • Commutation Relations, basis states, orbital angular momentum, the spherical harmonics

• Symmetries and Constants of Motion

  • The translation operator, the rotation operator, rotation of observables, scalar and vector observables, spinors, the rotation operator for a spin 1/2 particle

Reference: http://electron6.phys.utk.edu/qm1/Modules.htm

• A Particle in a Central Field

  • The asymptotic behavior of the radial functions, two interacting particles.

• Hydrogenic Systems

  • The hydrogen atom, eigenvalues and eigenfunctions, spectroscopic notation, hydrogenic systems.

• Diatomic Molecules

  • Motion of the nuclei, vibrational-rotational levels.

• Addition of Angular Momentum

  • Clebsch-Gordan coefficients, adding more than two angular momenta, rotation matrices, transformation properties of the spherical harmonics, the Wigner-Eckart theorem, the projection theorem.

• Gauge Transformations, Flux Quantization, Propagator

  • Gauge transformations in electromagnetism, the Aharonov-Bohm effect, magnetic monopoles, propagator and path integrals.

• Periodic Systems

  • Periodic and continuous systems, Electrons in a solid.

• Scattering

  • Scattering by a central potential, free spherical waves, partial waves, phase shifts,   the scattering cross section near a resonance, scattering length and effective range, frame transformations, integral scattering equation for stationary states, the Born approximation, the Yukawa potential, the Coulomb potential.

• Approximation Methods for bound states

  • Stationary perturbation theory, the perturbation of degenerate states, the variational method,

• The fine structure and hyperfine structure of H

  • The Dirac equation, the fine structure Hamiltonian, the hyperfine structure Hamiltonian.

• Time Dependent Perturbation Theory

  • Atoms interacting with an electromagnetic wave, transition selection rules

• Identical Particles

  • Permutation operators, Slater Determinants, atomic spectra, coupling schemes