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Test%201%20Solutions

# Test%201%20Solutions - EEE 352 Spring 2008 Test 1 1 A...

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EEE 352 – Spring 2008 Test 1 February 20, 2008 1. A particular quantum system is characterized by a wave function with the following form: x Axe x α ψ = ) ( for x 0. The wave function is zero for x < 0. Determine A, <x>, <x 2 >, <p>, <p 2 >, and x p. You may assume that A is positive and real. We first normalize the wave to find A as 2 / 3 3 2 0 0 2 3 2 0 2 3 2 0 2 2 2 2 4 2 8 8 1 α α α α α = = + = = = A A du ue e u A du e u A dx e x A u u u x Then ( ) 4 2 2 3 ) 2 ( 4 4 function wave real 0 3 8 1 4 2 3 4 1 4 2 2 0 2 2 2 2 3 0 2 2 2 3 2 2 0 4 2 0 2 4 3 2 0 3 0 2 3 3 h h h h α α α α α α α α α α α α α α α α α α = = = = = = = = = = = dx e x x dx xe x xe p p du e u dx e x x du e u dx e x x x x x u x u x Finally, α α α α 3 4 0 4 2 3 3 2 2 2 h h = = p x .

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