Chapter 5 - Identical Particles
The Intermediate Coupling Model

The photon-dressed electron

  • The photon re-invents itself
  • Just like SpongeBob clones himself
  • Crossed polarizers
  • Bosons and ants
  • Let there be light: take the rest of the week off!

    Two electron systems (Griffiths pp. 201-214)

    Wave Functions

  • Separation of uncoupled Schrödinger equations
  • Symmetric and antisymmetric products
  • Product of space and spin
  • Quantum coins
  • The exclusion principle

    Slater energies

  • Perturbed spin/space wavefunctions
  • Direct and exchange electron-electron
  • Two-center expansion
  • Invoke angular orthogonality
  • Fk and Gk expansions

    Magnetic energies (Griffiths p. 274)

  • Biot-Savart Law
  • Spin-orbit coupling
  • Electron-electron and spin-orbit perturbations

    Matrix formulation (Griffiths pp. 449-453)

  • Off-diagonal matrix
  • Transformation formulation
  • Diagonalization of 2x2 matrices
  • Application to sp
  • Term splitting
  • Experimental data

    Hund's rule (Griffiths pp. 216-218)

  • Fermi repulsion and Bose attraction?
  • Geometric exclusion and inclusion
  • Friedrich Hund
  • Magnetism on the half-shell
  • Ground states
  • continued

    Semiempirical formulation

  • Reduction of Slater parameters from data
  • Problem
  • Solution

    Computation of G1

  • Hydrogenic calculation of G1(2s,2p)
  • G1(2s,2p) (continued)
  • Higher n
  • Maple

    Exchange symmetries

  • Terms ruled out by exclusion
  • Carbon example
  • Matrix
  • Diagonalized
  • Splitting
  • p2 and p4 IC diagrams
  • Representation
  • Deduction of parameters
  • Problem
  • Solution
  • The Si sequence
  • Calibration lines

    Three electron systems

  • Three open-shell p electrons
  • p3 matrix diagonalization
  • Inversion of coefficients from known roots
  • p3 matrix diagonalization
  • Application
  • Matrices
  • Vectors and matrices
  • Matrix product
  • Compare with ab initio
  • P sequence
  • LS to jj

    Slater determinant (Griffiths p. 210)

  • Antisymmetrization: the Slater determinant
  • Paper size needed to specify wave functions

    Self-consistent field calculations

  • Potential energy with screening
  • Internal and external screening
  • 1-D radial probability distribution
  • Iterate effective potential
  • Schematic
  • EBK for the Many Body Problem
  • Y(QM) and Y(EBK)
  • Comparison with HF for Na seq
  • Screened hydrogenic parametrization of fs
  • Artifact in Cu seq

    • Relativistic Semiempirical Formulation

  • Relativistic Hamiltonian
  • Relativistic radial momentum
  • In terms of alpha
  • Repeat SCSCF
  • Collapse of the Maslov Perihelion
  • Calculated examples of turning points
  • Redistribution
  • Relativistic angle-action