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# quiz3 - Physics 2D Spring 2010 Quiz#3 Matter Waves...

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Physics 2D — Spring 2010 Quiz #3: Matter Waves Friday April 30 11:00am to 11:50am [Note: This is a closed-book exam. Only the use of 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: Binomial expansion: (1 + x ) n = 1 + n · x + n ( n - 1) 2 x 2 + ... k = 2 π/λ , ω = 2 πf , ¯ h = h/ (2 π ) de Broglie: E = ¯ , p = ¯ hk phase velocity: v p = ω/k group velocity: v g = dk Heisenberg’s uncertaity principle: Δ x · Δ p ¯ h/ 2 Schr¨ odinger’s equation: i ¯ h ∂t Ψ = - ¯ h 2 2 m 2 ∂x 2 Ψ + U ( x 1

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1. Short answers: [10/50 points total] (a) Explain how Newton’s second law is incompatible with Heisenberg’s uncertainty principle. Qualitatively, why is the uncertainty principle not important for macroscopic objects. [5 points] (b) State Born’s interpretation of the wave function Ψ( x, t ). Write down the normalization condition at a particular time t , and explain what the condition means. Why can’t the
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quiz3 - Physics 2D Spring 2010 Quiz#3 Matter Waves...

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