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Postulates

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.

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Postulates

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  1. 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 an of A. Postulate 5: The probability to get an is . After the measurement, the wavefunction collapes to (corresponding eigenfunction). Postulate 6: N identical particles. The wavefunctions are either symmentrical (bosons) or antisymmetrical (fermions).

  2. Orbital angular momentum + circ. perm. Commutation relations Eigenfunctions common to L2, Lz Spherical harmonics integers Orthonormality Raising, lowering operators

  3. One particle in a spherically symmetric potential H, L2, Lz commute Eigenfunctions common to H, L2, Lz Degeneracy Centrifugal potential Wavefunctions parity:

  4. Angular momentum + circ. perm. Commutation relations Eigenfunctions common to J2, Jz Integers or half-integers Angular momentum Addition of two angular momenta: Triangle rule L2, Lz ,S2, Sz commute L2, S2, J2, Jz commute Clebsch-Gordan coefficients

  5. One particle in a spherically symmetric potential Eigenfunctions common to H, L2, Lz , S2, Sz Eigenvalues Eigenfunctions common to H, L2, S2, J2, Jz Eigenvalues Also eigenfunctions to the spin-orbit interaction

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

  7. 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 rb(E), width h Fermi’s Golden rule For

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

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

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

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

  12. Many-electron atom Hc central field H1 perturbation antisymmetrical/ permutation of two electrons Slater determinant Pauli principle Electon configuration, periodic system etc.. Wavefunctions common to Hc, L2, Lz, S2, Sz 2S+1L Beyond the central field approximation: terms LS coupling jj coupling

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