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quiz6 - Physics 2D Spring 2010 Quiz#6 Friday:00am to...

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Physics 2D — Spring 2010 Quiz #6 Friday May 28 11:00am to 11:50am [Note: This is a closed-book exam. No calculator is allowed. The total score of this exam is 50 points. Points assigned to each problem is a guide to how many minutes you should spend working on it.] Possibly useful formulae: k = 2 π/λ , ω = 2 πf , ¯ h = h/ (2 π ) de Broglie: E = ¯ , p = ¯ hk Heisenberg’s uncertaity principle: Δ x · Δ p ¯ h/ 2 time-independent Schr¨ odinger’s equation for spherically symmetric potential in 3-dimension: - ¯ h 2 2 m 2 ψ + U ( r ) ψ ( r, θ, φ ) = E ψ ( r, θ, φ ) differential equation for the radial wave function R ( r ) resulting from separation of variable: ψ ( r, θ, φ ) = R ( r ) · Y ( θ, φ ) - ¯ h 2 2 m R 00 + 2 r R 0 + " U ( r ) + · ( + 1)¯ h 2 2 mr 2 # R ( r ) = E R ( r ) differential equation for the angular wave function Y ( θ, φ ) resulting from separation of vari- able: ψ ( r, θ, φ ) = R ( r ) · Y ( θ, φ ) " 2 Y ∂θ 2 + cot θ · ∂Y ∂θ + 1 sin 2 θ · 2 Y ∂φ 2 # = - · ( + 1) Y ( θ, φ ) expectation values of angular momenta:

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