QMGreensite_merged
17.4. DEGENERATEPERTURBATIONTHEORY 275 foralli,n<qwithi+=n,whichisgenerallynotthecase. Thewayoutofthisdilemmaistofirstnoticet ...
276 CHAPTER17. TIME-INDEPENDENTPERTURBATIONTHEORY 17.4.1 Diagonalizing theSubmatrix Equations(17.74)givetheperturbativesolutions ...
17.4. DEGENERATEPERTURBATIONTHEORY 277 17.4.2 Example-TheTwo-DimensionalHarmonicOscillator TheHamiltonianforaharmonicoscillatori ...
278 CHAPTER17. TIME-INDEPENDENTPERTURBATIONTHEORY andtheφm(x)andφn(y)areone-dimensionalharmonicoscillatoreigenstates. The totale ...
17.4. DEGENERATEPERTURBATIONTHEORY 279 tofindtworoots E±=± 1 2 β^2 (17.96) correspondingtoeigenstates φ+ = aφ 10 +bφ 01 φ− = cφ ...
280 CHAPTER17. TIME-INDEPENDENTPERTURBATIONTHEORY 17.4.3 Example - TheStarkEffect TheStarkEffectisasplittingofspectrallinesdueto ...
17.4. DEGENERATEPERTURBATIONTHEORY 281 wherea 0 = ̄h^2 /me^2 istheBohrradius. Thesecularequationisthen det[V −EI] = det ...
282 CHAPTER17. TIME-INDEPENDENTPERTURBATIONTHEORY TherearethreevaluesofEtoconsider: CaseI: E= 3 a 0 Matrixmultiplicationonthelef ...
17.4. DEGENERATEPERTURBATIONTHEORY 283 stillgivesa= 1 / √ 2,leadingtotheeigenstate |φ〉E 2 −= 1 √ 2 [ |φ 200 〉−|φ 210 〉 ] (17.124 ...
284 CHAPTER17. TIME-INDEPENDENTPERTURBATIONTHEORY ...
Chapter 18 Time-Dependent Perturbation Theory ThusfarwehavealwaysassumedthatthepotentialV(x)intheSchrodingerequa- tionistime-ind ...
286 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY agivenorbitalφn,whatistheprobabilitythattheincidentradiationwillresultin theelec ...
287 i ̄h dc(1)k dt = ∑ n 〈ψk|V|ψn〉c(0)n i ̄h dc(2)k dt = ∑ n 〈ψk|V|ψn〉c(1)n ... = ... i ̄h dc(km+1) dt = ∑ n 〈ψk|V|ψn〉c(nm) ... ...
288 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY or,using |ψn(t)〉 = e−iωnt|φn〉 〈ψn(t)| = eiωnt〈φn| (18.19) wehaveingeneral c (m) ...
18.1. HARMONICPERTURBATIONS 289 Againweimaginethatthesystemisinthestateψlatt≤0,sothatck(0)=c^0 k=δkl. Substituting(18.25)into(18 ...
290 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY ThesecondsurpriseisthatalthoughthetransitionfromEltoEkbyabsorbtionis mostprobabl ...
18.1. HARMONICPERTURBATIONS 291 ofthewaveisct, thenthephotonislocalizedwithinthisregionbeforeabsorbtion. Therefore,bytheUncertai ...
292 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY (as you surely know) standsfor “LightAmplification by StimulatedEmissionof Radia ...
18.1. HARMONICPERTURBATIONS 293 andnearlythesamematrixelements 〈φk′|v|φl〉≈〈φk|v|φl〉 (k′,k∈K) (18.43) Forexample,theelectronfinal ...
294 CHAPTER18. TIME-DEPENDENTPERTURBATIONTHEORY Wewillpostponeapplicationofthisruleuntilwestudyscattering. However,some examples ...
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