2
CONTENTS
PartI- Fundamentals
- TheClassicalState
Newton’sLawsandthePrincipleofLeastAction.TheEuler-Lagrangeequations
andHamilton’sequations.Classicalmechanicsinanutshell.Theclassicalstate. - HistoricalOriginsofQuantumMechanics
Black-bodyradiation,thephotoelectriceffect,theComptoneffect. Heisenberg’s
microscope. TheBohratom.DeBrogliewaves. - TheWave-likeBehaviourofElectrons
Electrondiffractionsimplified:the”double-slit”experimentanditsconsequences.
The wave equation for De Broglie waves, andthe Born interpretation. Why an
electronisnotawave. - TheQuantumState
HowdoestheelectrongetfromAtoB?RepresentationoftheDeBroglie”wave”
asapointmovingonthesurfaceofaunitsphere. Functionsasvectors,wavefunc-
tionsasunitvectorsinHilbertspace. Bra-ketnotation. TheDiracdeltafunction.
ExpectationvalueandUncertainty∆xinelectronposition. - Dynamics oftheQuantumState
Ehrenfest’sprinciple. Schrodinger’swaveequation. ThemomentumandHamil-
tonianoperators.Time-independentSchrodingerequation.Thefreeparticleandthe
gaussianwavepacket. Phasevelocityandgroupvelocity. Motionof aparticleina
closedtube. - EnergyandUncertainty
Expectationvalueofenergy,uncertaintyofmomentum. TheHeisenbergUncer-
taintyPrinciple. WhytheHydrogenatomisstable. Theenergiesofaparticleina
closedtube. - OperatorsandObservations
Probabilitiesfrominnerproducts. Operatorsandobservables,Hermitianopera-
tors. Statesof”zerouncertainty”; theeigenvalueequation. Commutators,andthe
generalizedUncertaintyPrinciple.