NRQM10finextra

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online