hwk8 - α(c Write down the equations for the continuity of...

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Physics 31: Homework #8 Due Thursday, March 27, 2008 Problem A: For this problem, you are to work out the solution for the wave function in a ±nite square well, for the case of an odd wave function. (In class, we did the case of an even wave function.) V = V 0 V =0 x -L /2 0 + L /2 E II I (a) Write down the explicit form of the time-independent Schroedinger equation in region I. Let ψ I ( x ) = sin kx ,whe re k 2 =2 mE/ ¯ h 2 , and explain why this ψ I ( x ) is the desired solution to the Schroedinger equation. (b) Write down the explicit form of the time-independent Schroedinger equation in re- gion II, and verify that ψ II ( x )= C exp( αx )+ D exp( - αx ) is a solution to this equation. What is
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Unformatted text preview: α ? (c) Write down the equations for the continuity of the wave function and its derivative at the point x = L/ 2. Solve the equations to ±nd the condition that must be satis±ed in order to have C = 0. Explain why there is a physical solution only for certain values of the energy E . Problem B: Find ∆ p for a particle in the ground state of the in±nite square well. Start with the exact expression in terms of the momentum operator. Do the following problems in Beiser: Chapter 5: 12, 19 (For problem 19, the answer given in the back of the book is exact. Show how to get it. )...
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