4.5 Consider reflection from a step potential of height Vo with E > Vo,but now with an infinitely high wall added at a distance a from thestep (see diagram):V(x)EV = VoV = 0x = 0x = ax(a) Solve the Schrödinger equation to find v/(x) for x < 0 and 0 ≤xa. Your solution should contain only one unknown constant.(b) Show that the reflection coefficient at x = 0 is R = 1. This isdifferent from the value of R previously derived without the infinitewall. What is the physical reason that R = 1 in this case?(c) Which part of the wave function represents a leftward-movingparticle at x < 0? Show that this part of the wave function is anSolutions of the one-dimensional time-independent Schrödinger equation103eigenfunction of the momentum operator, and calculate the eigen-value. Is the total wave function for x ≤ 0 an eigenfunction of themomentum operator?

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Answered: 4.5 Consider reflection from a step…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter7: Tunneling Phenomena

Section: Chapter Questions

Problem 2P

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Solve the following.
Consider the "step" potential: V(x) = (a) Calculate the reflection coefficient, for the case E 0. (b) Calculate the reflection coefficient for the case E > Vo. (c) For a potential such as this, which does not go back to zero to the right of the barrier, the transmission coefficient is not simply |F12/A2 (with A the -Vo AV(x) Scattering from a "cliff" incident amplitude and F the transmitted amplitude), because the transmitted wave travels at a different speed. Show that T = E-Vo F1² E |A|² X for E> Vo. Hint: You can figure it out using Equation gantly, but less informatively-from the probability current ( What is T, for E Vo, calculate the transmission coefficient for the step potential, and check that T + R = 1.
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