HW04 & Solutions

# HW04 & Solutions - ECE 306 Homework Set#4 Spring...

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ECE 306 Homework Set #4 Spring 2005 (Due 12 noon, Wednesday, February 22, 2005) 1. Consider a particle of mass m in a potential field V(x). (a) Show that the time variation of the expectation value of the momentum is given by: m p x dt d x = (b) Prove that the time variation of the expectation value of the momentum is given by: x x F dx dV p dt d = = , which is known as Ehrenfest’s theorem. 2. Sketch the de Broglie wavelength versus the kinetic energy up to 10 eV ( = 1.6e- 18 Joules) for (a) electrons, protons and (b) neutrons and compare these results with the corresponding result for photons 3. Suppose we know that there is a free particle initially located in the range –a < x < a with a spatially uniform probability. (a) Give the normalized state function Ψ (x, t = 0) of the particle in the Schroedinger- representation. Assume the phase of the wave function is arbitrarily chosen to be zero. (b) Give the corresponding momentum representation of the particle.

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