NRQM10finextra

# NRQM10finextra - Physics 216 Final Exam Extras Spring 2010...

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Unformatted text preview: Physics 216 Final Exam Extras Spring 2010 This sheet contains additional information to help you solve the problems of the final exam more efficiently. 1. For β = 0, the unperturbed n = 2 energy eigenfunctions are given by: ψ 200 ( vector r ) = 1 √ π parenleftbigg 1 2 a parenrightbigg 3 / 2 parenleftbigg 1 − r 2 a parenrightbigg e − r/ (2 a ) , ψ 210 ( vector r ) = 1 √ 2 π parenleftbigg 1 2 a parenrightbigg 3 / 2 r a e − r/ (2 a ) cos θ , ψ 21 ± 1 ( vector r ) = ∓ 1 √ 8 π parenleftbigg 1 a parenrightbigg 3 / 2 r a e − r/ (2 a ) sin θ e ∓ iφ , where a = planckover2pi1 2 / ( me 2 ). You will also need to compute some integrals. One useful integral is: integraldisplay ∞ r n e − r/a dr = a n +1 n ! , where n is a non-negative integer. Finally, the following matrix elements of L x will be needed for part (c): ( ℓ ′ m ′ ℓ | L x | ℓ m ℓ ) = 1 2 planckover2pi1 δ ℓℓ ′ braceleftbig [( ℓ − m ℓ )( ℓ + m ℓ +1)] 1 / 2 δ m ′ ℓ , m ℓ...
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NRQM10finextra - Physics 216 Final Exam Extras Spring 2010...

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