quiz4 - Physics 2D Spring 2010 Quiz #4: 1D Schrdinger Eqn o...

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Quiz #4: 1D Schr¨ odinger Eqn Friday May 7 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: time-dependent Schr¨ odinger’s equation: i ¯ h ∂t Ψ = - ¯ h 2 2 m 2 ∂x 2 Ψ + U ( x time-independent Schr¨ odinger’s equation: - ¯ h 2 2 m 2 ∂x 2 ψ + U ( x ) ψ ( x ) = ( x ) expectation values: h x m i = R -∞ dxx m P ( x ) standard deviation: Δ x = q h x 2 i - h x i 2 , Δ p = q h p 2 i - h p i 2 energy levels of the harmonic oscillator: E n = ( n + 1 2 c for n = 0 , 1 , 2 ,... , with ω c being the frequency of the classical oscillator. sin( θ ) = 0 for θ = 0 , ± π, ± 2 π, 3 π,. .. cos( θ ) = 0 for θ = ± π/ 2 , ± 3 π/ 2 , ± 5 π/ 2 ,... R
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quiz4 - Physics 2D Spring 2010 Quiz #4: 1D Schrdinger Eqn o...

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