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 asBandJ26.08.02 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 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 A little about groups 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 thefor 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 NOTE ABOUT THE SELFCONSISTENT FIELD (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

autumn term 1996. One can see a detailed description of all the topics discussed.

Here we added some details about the collisions.