Unformatted text preview: Problem Set #4 Due: 5 pm, Friday, 10/7/11 1.) Time Evolution of a Wave Function To get a sense of how a wave function evolves, plot the real and imaginary parts of the wave function Ψ(x, t), and |Ψ(x, t)|2 for Problem 1 of PS3, after the wall has been moved from x = L to x = 2L, at six different times: t = 0, T0/5 , 2T0/5, 3T0/5, 4T0/5, T0 where T0 is the period of the ground state of the well with length = 2L. In the Fourier expansion, you only need to include three terms: the ground, first excited and second excited states of the expanded well. Griffiths: 2.21 (Free Particle) 2.29 ((Odd Bound State Solutions to FSW) 2.22 (Stationary Gaussian Packet) 2.32 (FSW Transmission Coefficient) Compare and contrast the following two problems from Griffiths, and explain whether the λ/2 shift occurs at the potential step-‐up or the step-‐down? 2.34 (Step-‐up Potential) 2.35(Step-‐down Potential) 2.33(Potential Barrier Transmission Coefficient) ...
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- Fall '09
- mechanics, Problem Set, imaginary parts, wave function, different times, Step-‐down Potential