Postulates Postulate 1: A physical state is represented by a wavefunction. The probablility to find the particle at within is. Postulate 2: Physical quantities are represented by Hermitian operators acting on wavefunctions. Postulate 3: The evolution of a wavefunction is given by the Schrödinger equation. Postulate 4: The measurement of a quantity (operator A) can only give an eigenvalue a n of A. Postulate 5: The probability to get a n is. After the measurement, the wavefunction collapes to (corresponding eigenfunction). Postulate 6: N identical particles. The wavefunctions are either symmentrical (bosons) or antisymmetrical (fermions).

Quantum mechanics If H is time-independent Time-independent Schrödinger equation: H   t  e -iEt A, B, C,... Commutating Hermitian operators There exists a common set of orthormal egenfunctions

Orbital angular momentum + circ. perm. Commutation relations Eigenfunctions common to L 2, L z Spherical harmonics integers Raising, lowering operators Orthonormality

One particle in a spherically symmetric potential H, L 2, L z commute Eigenfunctions common to H, L 2, L z Centrifugal potential Degeneracy Wavefunctions parity:

Angular momentum + circ. perm. Commutation relations Eigenfunctions common to J 2, J z Integers or half-integers Addition of two angular momenta: Angular momentum Triangle rule L 2, L z,S 2, S z commute L 2, S 2, J 2, J z commute Clebsch-Gordan coefficients

One particle in a spherically symmetric potential Eigenfunctions common to H, L 2, L z, S 2, S z Eigenvalues Eigenfunctions common to H, L 2, S 2, J 2, J z Eigenvalues Also eigenfunctions to the spin-orbit interaction

Time-independent perturbation theory known ? Approximation ? Non-degenerate level Degenerate level (s times) First diagonalize H´ in the subspace corresponding to the degeneracy

Time-dependent perturbation theory known System in a at t=0 Probability to be in b at time t? Constant perturbation switched on at t=0 Continuum of final states with an energy distribution  b (E), width  For Fermi’s Golden rule

One particle in an electromagnetic field (I) Plane wave a b Absorption Stimulated emission Line broadening

One particle in an electromagnetic field (II) a b Absorption Dipole approximation Selection rules Oscillator strength

One particle in a magnetic field Paschen-Back effect Anomal Zeeman effect Zeeman effect

Quadratic Stark effect (ground state) One particle in an electric field Tunnel ionisation Linear Stark effect

Many-electron atom P identical particles  antisymmetrical or symmetrical /permutation of two electrons  antisymmetrical Postulate 6: N identical particles. The wavefunctions are either symmetrical (bosons) or antisymmetrical (fermions).

Many-electron atom H c central field H 1 perturbation Slater determinant Pauli principle Wavefunctions common to H c, L 2, L z, S 2, S z 2S+1 L Electron configuration, periodic system etc.. terms

Many-electron atom H c central field H 1 perturbation Slater determinant Pauli principle Wavefunctions common to H c, L 2, L z, S 2, S z 2S+1 L Beyond the central field approximation: LS coupling jj coupling antisymmetrical/ permutation of two electrons Electon configuration, periodic system etc.. terms