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.

Lectures:
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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
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

09.09.02 2-electron atoms continue
spin
( 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

Selfconsistent field method

23.09.02 Hartree-Fock method: what needed
Functional derivatives
(Variations)
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
(Variations)
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
equations

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)
- 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
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
Coherent states: web-browser 'applet'
Coherent states

31.10.02  Coherent states
Laser - Doppler cooling - start Junbai here
Strong laser fields relations
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

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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