pset02

# pset02 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall, 2002 Professor Robert W. Field Problem Set #2 DUE : At the start of Lecture on Friday, September 20. Reading : Merzbacher Handout, pp. 92-112. Problems : 2 a x , 1. ψ 1 () = bx x 0 ) 2 + c 2 ab, and c are real 2 ( x A. Normalize ψ 1 in the sense −∞ | ψ | 2 dx = 1. B. Compute values for x , x 2 , and x for 1 ( x ). C. ( optional ) Compute values for k and k for ψ 1 ( k ), where ψ 1 () is the k Fourier transform of ψ 1 ( x ). [If you choose not to do this problem, state what you expect for the form of Ψ 1 (k) and the magnitude of k.] 2 ( x 2. ψ 2 = e cx b ) 2 e i α ( x ) where c , b , and α ( x ) are real. Use the stationary phase idea to design α ( x ) in the region of x near x = b so that k = k 0 0. 3. Merzbacher, page 111, #2. 4. The following problem is one of my “patented” magical mystery tours. It is a very long problem which absolutely demands the use of a computer for parts F and G. There are many separate computer programs that you will need to write for this problem. I urge you to divide the labor into smaller groups, each responsible for a different piece of programming. I believe that the insights you will obtain from

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pset02 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum...

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