prob set 3

prob set 3 - PHYS 271 2009: Problem Set 3 Due Friday, Feb....

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PHYS 271 2009: Problem Set 3 Due Friday, Feb. 13, 2009 at the start of class. Problem sets are to be done individually. Be sure to put your name and student number on your assignment; problem sets without a name will not be graded . For all problems, be sure to fully explain what you are doing using words . 1. A particle in one-dimension moves in some unknown potential energy V ( x ) . One ±nds that it is described by a wavefunction ψ ( x,t )= e - iωt cos( kx ) where ω = Ak 2 + B . Here, A and B are constants. You can assume that this is a good wavefunction, meaning it is a solution to the Schrodinger equation. (a) What units must the constant A have? What units must the constant B have? (b) How does the mass of the electron depend on the constants A and B ? (c) Find an expression for the potential energy V ( x ) in terms of the constants A and B . 2. For this problem, we will consider an electron living in one spatial dimension which is restricted to the region between x =0 and x = L . The following is a wavefunction that could describe our particle:
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