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Unformatted text preview: PHYS 271: Problem Set 4 Due Friday, Mar. 13, 2009 at the start of class. For each question, be sure to explain clearly your rationale, and to show your work. 1. An electron is trapped in a funny looking potential well, described by the potential energy: U ( x ) = U x <- U ( 1- x / L )+ x > Here, U is a constant positive energy, and L is a constant with the units of length. Potential wells constructed using stacks of semiconductor material usually have this form. Suppose our particle has a definite energy E =- U / 2. (a) Make a graph of U ( x ) . What regions of space are classically forbidden to our particle? Explain why. (b) Classically, describe what kind of motion our particle will do while stuck in the well, using the fact that its energy is E =- U / 2. Will its speed be constant? (c) Make a sketch of the real part of the particles wavefunction. Clearly indicate the important points in your sketch. If in some region of space the wavefunction is oscillating, clearly indicate what thein your sketch....
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