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1 PHYSICS 430 Lecture Notes on Quantum Mechanics J. Greensite PhysicsandAstronomy Department San FranciscoStateUniversity Fall 2 ...

2 CONTENTS PartI- Fundamentals TheClassicalState Newton’sLawsandthePrincipleofLeastAction.TheEuler-Lagrangeequations andHamilto ...

3 PartII- Exact Solutions RectangularPotentials Qualitative behaviorof energyeigenstates. Why bound stateenergies aredis- crete ...

4 PartIV- Approximation Methods Time-IndependentPerturbationTheory Time-DependentPerturbationTheory Adiabatic,harmonic,and”sudd ...

5 APOLOGIA ThesearemylecturenotesforPhysics 430 and431,writtenanumberofyears ago. Theyarestillabitincomplete: Chapters 19 and 20 ...

6 ...

Chapter 1 The Classical State Inthefirstquarterofthiscentury,itwasdiscoveredthatthelawsofmotionformulated byGalileo,Newton,Lagra ...

8 CHAPTER1. THECLASSICALSTATE thistrajectoryexactly,butwewouldliketodevelopamethodwhichcanbeapplied toaparticlemovinginanypotent ...

1.1. BASEBALL,F=MA,ANDTHEPRINCIPLEOFLEASTACTION 9 andintegralsbysums ∫t 0 +∆t t 0 dtf(t)→ N∑− 1 n=0 !f(tn) (1.5) wheref(t)isanyf ...

10 CHAPTER1. THECLASSICALSTATE sothatF=macanbeinterpretedasaconditionthatacertainfunctionofxnshould bestationary.Letusthereforei ...

1.1. BASEBALL,F=MA,ANDTHEPRINCIPLEOFLEASTACTION 11 Problem: Dyre’sDilemma^2 Indiscussingthemotionofthebaseball, wehave beenignor ...

12 CHAPTER1. THECLASSICALSTATE 1.2 Euler-Lagrange and Hamilton’s Equations Inbrief,theEuler-Lagrangeequationsarethesecond-orderf ...

1.2. EULER-LAGRANGEANDHAMILTON’SEQUATIONS 13 wheretheLagrangianfunctionforthebaseballis L[x(t),x ̇(t)]= 1 2 mx ̇^2 (t)−V[x(t)] ( ...

14 CHAPTER1. THECLASSICALSTATE wherewehaveapplied(1.24).Next,differentiatingHwithrespecttox, ∂H ∂x = p ∂x ̇(x,p) ∂x − ∂L ∂x − ∂L ...