Final & Solutions

# Final & Solutions - ECE 306 Final Examination Spring...

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ECE 306 Final Examination Spring 2005 (3:00 to 5:00 PM, May 13, 2005. Open book and open notes.) 1. Consider the wave function: + > < + < < = 2 / ; 2 / 2 / 2 / 0 2 sin ) , ( / a x a x a x a for e a x A t x h iEt π ψ (a) Normalize this wave function (i.e. find A) and plot the space dependence of this wave function. (b) Verify that the above wave function is a solution to the Schroedinger equation in the region –a/2 < x < +a/2 for a particle which moves freely through the region but which is strictly confined to this region that is bounded by two impenetrable walls at x = ±a/2. (c) Determine the value of the total energy E of this state of the particle in the box defined between the two walls at x = ±a/2. Is this state the ground state of the particle in the box? Give the ground state energy of the particle in this box. (d) Calculate the expectation values of x and the linear momentum p x for the particle associated with the wave function given above in this problem.

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• Spring '05
• TANG
• wave function, Eqs, 12 erg

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