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PHYSICS 430 Lecture Notes on Quantum Mechanics

(C) ,thephotoelectriceffect, :the double-slit , wave , <x>andUncertainty , , zerouncertainty ; , , ,resonance, ; ,Symmetry, , ; , ; ,Fermions, , ,harmonic,and sudden nearlyclassical ,squarewell, paradox .Fasterthanlight?Bell s guidingwaves . consistenthistories seffect, , :Chapters19and20remaintobewritten, , ,itwasdiscoveredthatthelawsofmotionformu latedbyGalileo,Newton,Lagrange,Hamilton, Maxwell,andmanyothers,wereinadequatetoex plainawiderangeofphenomenainvolvingelect rons,atoms, ,anewtheory(togetherwithanewlawofmotion) ,anditisnowthebasicframeworkforunderstan dingatomic,nuclear,andsubnuclearphysics, aswellascondensed-matter(or solid-state ) (duetoGalileo,Newton,..) , ,whoseformulationbegins(butdoesnotend!)w ithNewton slawF= ,F=ma, ,orperhapsafewseconds, ,asafunctionoftime,asx(t); ,thenanytrajectoryhastheformofaparabola( inauniformgravitationalfield,neglectinga irresistance), ,ifwerequirethatthebaseballreturnstoyour handexactly tsecondsafterleavingyourhand, ,butwewouldliketodevelopamethodwhichcanb eappliedtoaparticlemovinginanypotentialf ieldV(x).

F = ma, which is actually a second-order differential equation m d2x dt2 = − dV dx (1.1) It is useful to reexpress this second-order equation as a pair of first-order equations dx dt = p m dp dt = − dV dx (1.2) where m is the mass and p is the momentum of the baseball. We want to find the solution of these equations such that x(t 0) = X ...

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