The course started Aug. 26th, 2002
There is a new version of the page about The AMOS report . This text can be of interest, it shows the relevance of atomic, molecular and optical sciences.


The book of Bransden and Joachain is referred as BandJ

26.08.02 Review of the topics, examples, highlights

02.09.02 One electron atoms
         - history: from Greeks to Bohr
         - spectra, prisms, rainbows
         - textbooks
         - Bransden and Joachain (BandJ p. 128-145, secs. 3.1 to 3.3)
         - Schrödinger equation, origin
         - Basic formulae
         - Atomic units
         - Two matlab programs
            1. Norwegian version of wavefunctions
            (downloads are understandable)
            2. Spherical harmonics

05.09.02 close one electron
         started 2-electron atoms
         - two particle quantum mechanics
         - spin
         -symmetric and antisymmetric wavefunctions

         for 1. electron problem
         - some computer demos
         Norwegian version of wavefunctions
         (downloads are understandable)

09.09.02 2-electron atoms continue
            ( sidelook: What is Spintronics)
         S=0 antisymmetric S=1 symmetric
         (s1.s2 term, S=s1+s2, S^2  etc
          also: triplet symmetric, singlet antisymmetric,
          ... without calculations)
         BandJ pages: 249-255
         Ground state of Helium
         Twice 1s state -1/2 (Z^2) x 2

         Evaluation of 1/| r1 - r2 |
         Multipole expansion

         Evaluation of M.E. of 1/| r1 - r2 |   ->  5/8 Z

         Variational method (vary in which effective z electrons are)
         Scaling arguments
         -1/2 Z^2  = 1/2 Z^2 - Z^2
                     (kin)     (pot) (see BandJ, p 145, 3.4 ... Virial theorem)
         for z!=Z:
         E(1s,z,Z)=1/2 z^2 - Zz
         1/| r1 - r2 |   ->  5/8 z
         Eg.s.(z,Z)= 2 (1/2 z^2 - Zz) + 5/8 z
         Take derivative -> 0  ---> z=Z-2/16

         Parahelium (singlet) orthohelium (triplet)
         Explanation why in S=1 states repulsion small!  (BandJ p. 266)
         --- Ferromagnetism: see page 282)

12.09.02  NO LECTURE
          (no participants)

16.09.02 Finish 2-electron atoms
         Hylleraas wavefunctions for groun state
         excited states - direct and exchange term
         Autoionizing states (review)

19.09.02 Many-electron atoms
         Why the simple spin picture is not applicable
         A little about groups

         Selfconsistent field method

23.09.02 Hartree-Fock method: what needed
         Functional derivatives
         Minumum of functions with constraints
         Variational principle for Schr.Eq.

27.09.02 (lecture from 23.09.02 repeated)
         Hartree-Fock method: what needed
         Functional derivatives
         Minumum of functions with constraints
         Variational principle for Schr.Eq.

30.09.02 Hartree-Fock method
         (Selfconsistent field method improved)

         Evaluation of the  
         for Slater determinant
         How does the N*(N-1)/2 sum over coordinate pairs
         become the sum over orbital pairs?
         The reduction of 1/2 (N (N-1))(N!)^2 terms
         to the correct number

         Applying the variational procedure
             -> Hartree-Fock equations

03.10.02 The variatinal principle: The direct term
         and the exchange term in Hartree Fock

         The exchange potential -> nonlocality
         Nonlocal potentials
          is not always V(x) Psi(x)
         Nonlocal potentials and 'velocity dependent' interaction

         Existing solutions and The Periodic system

07.10.02 Periodic System, the orbital energies
         features of the coulomb potential lost by addition of W(r)
         Qualitative argument for the sequence
         1s 2s 3p 4s 3d .....
         How in Ionic systems? Uranium 64+ ?

         Beyond independent electrons

         Expansion of Psi(x1,x2) in a double sum
         Configuration mixing

         Configuration mixing
         (materials here)

10.10.02 Interaction of atoms and electromagnetic field
         Time dependent quantum mechanics
         - two potential wells (oscillating probability)
         - decaying state (quasicontium)
         Quantization of extended systems
         - eigenmodes
         - harmonic oscillator
         Creation and annihilation operators
         (algebraic formulation, harmonic oscillator)

14.10.02 Interaction of atoms and electromagnetic field
         Fermi Golden Rule
         Golden Rule Simulator
         (old version: A picturebook about the model )
         Charged particle in electromagnetic field (1)

         Decaying system: constant rate w and the model
         Density of states in Fermi Golden Rule

17.10.02 Time dependent perturbation theory
         B+J pages 111-116
         Decaying system: constant rate w
         Decaying system: change from t-squared to t-linear

         modification of the

            w = dP/dt  --> dP/dt= w P

         exponential decay
         Modification of Perturbation theory line widths
         Line width: B+J pages 183-185

         Gaussian and Lorentzian on logarithmic scale

21.10.02 The overview:
         - model: Emission of light: shift from excited state of atom
           to excited state of the field
         - Electromagnetic field: extended (continuous) system; eigenmodes
           system of independent, de-coupled eigenmodes,
         - creation and anihilation operators.
         - Time dependent quantum mechanics:
           one isolated level embedded in (quasi-) continuum.
         - Time dependent perturbation theory
         - the transition rate (probability change per time unit)
         - Fermi Golden Rule
         - Concept of line width, line shape

         Remaining part for this lecture:
         - Hamiltonian of charged particle in el.mag. field
           (B+J appendix 6, page 629)
         - Resulting interaction particle-radiation field
         - Density of states evaluation

         - Analysis of the whole emission proces
         - Evaluation of line widths, lifetimes

24.10.02  Einstein coefficients (see book)
          Principles of laser (see book)

28.10.02  Principles of laser
          (see also water models)
          Coherent states (a note will come; see fys201)

Computer exercises:

          Golden Rule simulator
                 Matlab codes:
                    ndgolden.m new 2001, with delay for fast computers
                    twogolds.m two continua, with delay
                    dialog.txt a little diagonalization exercise
                 Pictures and texts
                    pictures from the runs
                    Picturebook about Golden Rule Simulator
          Coherent states: web-browser 'applet'
                    Coherent states

31.10.02  Coherent states
          Laser Cooling (see also Junbai's TALK)
          Laser - Doppler cooling - start Junbai here
          Strong laser fields relations
          Download a note on strong field in PDF and postscript
          Also source available above
          Laser light with atomic field strength

04.11.02  No lecture

07.11.02  No lecture

11.11.02  No lecture

14.11.02  Molecules
          Born-Oppenheimer Approximation (separate motions)
          Electronic levels with fixed nuclei
          Correlation diagrams
          Total energy as function of positions of the nuclei
          Equillibrium, bonding, antibonding
          Pictures to molecular states

18.11.02  Molecules
          Energetic relations, electronic, vibrational, rotational spectra
          vibrational, rotational spectra, features
          applications of molecular physics

          Atomic collisions
          Cross sections
          Potential scattering; Green's function, partial waves, Born approx.
          Experimental methods, beams, detectors, coincidence techniques

21.11.02  Atomic collisions
          Processes in atomic collisions
              excitation, ionization, electron exchange
          Description of collisions
          Green's function, partial waves, Born approximation
          Born approximation: elastic scattering from an atom
          Generalisation (qualitative) to excitation of an atom

          Semiclassical methods = classical motion of nuclei
          Time dependent perturbation theory
          Cross sections from semiclassical methods

          Atomic Collisions note from 1997
          a. The concept of the Cross Section
             built on simple presentation of POTENTIAL SCATTERING
             Greens function - Born Approximation:
          b. Electron Collisions, using Born Approximation
             ( how is the potential scattering formula for cross section
               modified for  elastic scattering pf electrons from a
               hydrogen atom - formally similar to the 2 electron atoms)
              ( and how this is then modified to include the possibility of
               excitation, i.e. change of STATE OF THE ATOMIC ELECTRON )
          c.  Atomic (massive projectiles)
              Often the classical trajectory method is used
              Time dependent Schrodinger Equation  for H = H0 + V(t)
              where V(t) = V(R(t))  ->  R(t) is the classical trajectory
           Notes about Bransden and Joachain presentations

25.11.02  Relativity in atomic physics
          Dirac Equation......

28.11.02  Atomic spectra, effects of fields
          fine structure, hyperfine structure
          Stark, Zeeman

Preliminary version of our Atom-Light "book" in PDF format

It might be of interest to have a look through the notes from 1996 and 1997

There were no new electronic pages set up during 1998-2001,
but we have produced a lots of new electronic material which will
gradually be linked here.

So, please, visit this page regularly

  • 1996-notes about FYS 287: Where What When
    autumn term 1996. One can see a detailed description of all the topics discussed.
  • 1997 NEWS about FYS 287: Where What When
    Here we added some details about the collisions.