MSE Problem Set 4 2011 [QM ExpVal PIB]

# MSE Problem Set 4 2011 [QM ExpVal PIB] - MSE 310/ECE 340...

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MSE 310/ECE 340 Dept. of Materials Science & Engineering Electrical Properties of Materials Fall 2011/Bill Knowlton 1 Problem Set 4 (Show all work for all problems) 1. In class, we considered the radial wave function of an electron in a hydrogen atom given by:  o r a re a. Explain the symmetry (i.e., geometry) that the electron experiences. That is, if you were to normalize the wave function, what coordinate system would you use? Explain. b. Using part a , normalize the wave function. That is, find the normalization constant and provide the normalized wave function. 2. The Heisenberg uncertainty principle is given by: 2 x xp   where Δ x and Δ p x are given by expectation values of x and p x . Specifically, they are given by: 2 2 2 2 ˆˆ and xx x xxx p pp  For the particle in the box problem, determine the Heisenburg Uncertainty Principle by finding each expectation value separately. That is: a. Find x . Simplify your answers as much as possible. Note: you will need to normalize the wave
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