PHYS 271 2009: Problem Set 3Due 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 aname 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 energyV(x). One ±nds that it is described by a wavefunctionψ(x,t)=e-iωtcos(kx)whereω=Ak2+B. Here,AandBare constants. You can assume that this is a good wavefunction, meaning it is a solution tothe Schrodinger equation.(a) What units must the constantAhave? What units must the constantBhave?(b) How does the mass of the electron depend on the constantsAandB?(c) Find an expression for the potential energyV(x)in terms of the constantsAandB.2. For this problem, we will consider an electron living in one spatial dimension which is restricted to the region betweenx=0andx=L. The following is a wavefunction that could describe our particle:
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