QMGreensite_merged
18.2. ADIABATICPERTURBATIONS 295 SubstitutingthisexpressionforRand∆Rinto(18.54) n = 1 2 π ( 2 mL^2 π^2 ̄h^2 ) E 1 2 ( 2 mL^2 π^2 ...
296 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY weget ψ(x,t)=e−iωlt φl(x)+λ ∑ k(=l 〈φk|V(t)|φl〉 E(0)l −Ek^0 φk(x) (18.64) ...
18.2. ADIABATICPERTURBATIONS 297 NotethatsinceEl(t)variesintime,theenergyofthesystemisnotconserved, evenafterlongtimes. But,youm ...
298 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY 18.2.2 Validity Beforeleavingthetopic,itsnecessarytohavesomecriterionforthevalid ...
18.3. SUDDENPERTURBATIONS 299 atamoment(t= 0 −)justbeforetheperturbationisswitchedon. Withthisinitial condition,wewanttoknowwhat ...
300 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY Then c 0 = 〈φ′ 0 |φ 0 〉 = ( m π^2 ̄h^2 ) 1 / 4 (kk′)^1 /^8 ∫ dxexp [ − 1 2 ( √ m ...
Chapter 19 The WKB and Variational Methods (InPreparation) 301 ...
302 CHAPTER19. THEWKBANDVARIATIONALMETHODS ...
Chapter 20 Scattering Theory 303 ...
304 CHAPTER20. SCATTERINGTHEORY ...
Chapter 21 Quantum Mechanics as Linear Algebra Ihavestressedthroughoutthecoursethatphysicalstatesinquantummechanicsare represent ...
306 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA 21.1 Review of Vectors and Matrices AD-dimensionalcolumnvectorisasetofDcomplexnum ...
21.1. REVIEWOFVECTORSANDMATRICES 307 or,foreachcomponentofthetransformedcolumnvector, vi′= ∑D j=1 mijvj (21.9) Likewise,amatrixt ...
308 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA where !i 1 i 2 ...iD= +1 if i 1 i 2 ...iD anevenpermutationof 123 ...D − ...
21.1. REVIEWOFVECTORSANDMATRICES 309 whereHisanHermitianmatrix. TheEigenvalueEquationforamatrixM istherelationMu=λu,or [ m 11 m ...
310 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA or,inthecaseofaD×Dmatrix,solvetheDsimultaneousequations ∑D j=1 miju(jn)=λnu(in) ( ...
21.1. REVIEWOFVECTORSANDMATRICES 311 Therefore λ∗nu(n)·u(m)=λmu(n)·u(m) (21.42) Forn=m,thisimplies λn isrealforalln (21.43) whic ...
312 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA so λ 1 =+1 u^1 = 1 √ 2 [ 1 −i ] (21.51) Theprocedureforλ 2 =− 1 isidentical: [ 0 ...
21.2. LINEARALGEBRAINBRA-KETNOTATION 313 Laws ofmotionarefundamental,reference framesarenot, andoneof the ob- jectivesof vector ...
314 CHAPTER21. QUANTUMMECHANICSASLINEARALGEBRA whereaandbareanyconstants. Thereisalsodefinedaninnerproduct<u|v> betweenbra ...
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