3
PartII- Exact Solutions
- RectangularPotentials
Qualitative behaviorof energyeigenstates. Why bound stateenergies aredis-
crete,whyunbound eigenstatesoscillate. Steppotentials. Thefinite squarewell.
Tunnelling,resonance,andtheRamsauereffect. - TheHarmonicOscillator
Motivation: themostimportantexampleinphysics.Raisingandloweringopera-
tors;algebraicsolutionfortheenergyeigenvalues.Hermitepolynomials. - TwoDimensions,Symmetry,andDegeneracy
The Parity operator in onedimension. The particle ina square. The two-
dimensionalharmonicoscillator.Thequantumcorral. - TheSpectrumofAngularMomentum
Motionin 3 dimensions. Angularmomentumoperators,andtheircommutation
relations.Raisingandloweroperators;algebraicsolutionfortheangularmomentum
eigenvalues. Sphericalharmonics. Therigidrotator,andtheparticleinaspherical
box. - TheHydrogenAtom
Seriessolutionforenergyeigenstates. Thescaleoftheworld.
PartIII- AspectsofSpin
- ElectronSpin
Evidencefor electron spin: the Zeeman effect. Matrixrepresentation of spin
angularmomentum;Paulispinmatrices. Spin-orbitcouplingasmotivationtoadd
angularmomentum. - TheAdditionofAngularMomentum
Thegeneralmethod.Atomicfinestructure. - IdenticalParticlesandthePeriodicTable
Bosons,Fermions,andthePauliExclusionPrinciple.TheHartreeapproximation
formany-electronatoms.ThePeriodicTable. - LiveWiresandDeadStars
TheKronig-Penneymodelofelectronbandstructure. Thefreeelectrongasand
thefermienergy.Degeneracypressure,andtheradiiofneutronstars.