PHY801:
Survey of Atomic and Condensed Matter Physics
Spring 2020
Review for Exam 1
Version: October 3, 2019
Topics covered in the first part of the course and Midterm Exam 1:
- One-electron atoms
- Hydrogen atom and hydrogenic atoms: energy spectrum, scaling,
degeneracy, fine structure corrections
(mass-velocity and spin-orbit interaction)
- Atomic units
- Variational principle: Etrial(α)=min.
- Hellmann-Feynman Theorem: ∂E∕∂λ =
<ψ|∂H(λ)∕∂λ|ψ>
- Virial theorem.
- Many-electron atoms
- Electronic configuration of many-electron atoms.
- Multiplet structure of many-electron atoms. L-S coupling scheme.
- Hund's rules determining the lowest energy multiplet.
- Magnetism of atoms
- Langevin diamagnetism.
- Open-shell paramagnetism (spin and orbit contributions).
- Landé g-factor gJ and total effective magnetic moment
(depends on gJ and J).
- Magnetization of monatomic gases. Magnetic susceptibility. Brillouin function.
- Molecules
- Born-Oppenheimer or adiabatic approximation.
- H2+ molecular ion. Binding energy of
H2+.
- H2 molecule and two-electron systems.
- Total wave function in terms of space and spin states.
- Spin wavefunctions, spin singlets and spin triplets.
- Antisymmetry of the total wave-function under interchange of space and spin coordinates.
- Bonding (gerade) and anti-bonding (ungerade) molecular orbitals
for H2.
- Concept of bonding and anti-bonding molecular orbitals expressed
in terms of atomic orbitals.
- Total energy as a function of interactomic distance
and molecular binding energy.
- Covalent bonds in H2, B2, ... molecules.
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2020.01.05 (Sunday) 16:11:48 EST
by David Tomanek -
tomanek@msu.edu