MSE 310/ECE 340Dept. of Materials Science & Engineering Electrical Properties of MaterialsFall 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: orarea.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: 2xxp where Δxand Δpxare given by expectation values of xand px. Specifically, they are given by: 2222ˆˆandxxxxxxpppFor the particle in the box problem, determine the Heisenburg Uncertainty Principleby 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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