quiz5 - Physics 2D Spring 2010 Quiz#5 Friday:00am to...

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Physics 2D — Spring 2010 Quiz #5 Friday May 14 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: Heisenberg’s uncertainty principle: Δ x · Δ p ¯ h/ 2 time-independent Schr¨ odinger’s equation in 1-dimension: - ¯ h 2 2 m d 2 dx 2 ψ + U ( x ) ψ ( x ) = ( x ) transmission coefficient through square barrier of height U 0 and length L : T ( E ) exp - 2 q 2 m ( U 0 - E ) ¯ h L . 1
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1. Short Answers: [12 total points] (a) What is the condition on a finite square well of depth U 0 and width L in order for a particle of mass m trapped in it to regard the well as similar to an infinite square well? why? [4 points] (b) Sketch and explain qualitatively the difference between the ground state wave function of a very shallow and a very deep square well. Indicate the regions that are classically forbidden. [4 points] (c)
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