MSE Problem Set 4 Solutions 2011 [QM ExpVal PIB]

MSE Problem Set 4 Solutions 2011 [QM ExpVal PIB] - MSE...

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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 Solutions (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. Since a hydrogen atom is a sphere, the easiest coordinates to use to integrate over a sphere would be to use spherical or polar coordinates.
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MSE 310/ECE 340 Dept. of Materials Science & Engineering Electrical Properties of Materials Fall 2011/Bill Knowlton 2 b. Using part a , normalize the wave function. That is, find the normalization constant and provide the normalized wave function. Using spherical coordinates:
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MSE 310/ECE 340 Dept. of Materials Science & Engineering Electrical Properties of Materials Fall 2011/Bill Knowlton 3
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MSE 310/ECE 340 Dept. of Materials Science & Engineering Electrical Properties of Materials Fall 2011/Bill Knowlton 4 2. The Heisenburg 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 
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This note was uploaded on 10/16/2011 for the course ENGINEERIN MSE 310 taught by Professor Billknowlton during the Spring '10 term at Boise State.

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MSE Problem Set 4 Solutions 2011 [QM ExpVal PIB] - MSE...

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