FinalExam-Fall2010

FinalExam-Fall2010 - Signature_ Name_ Phys 401 Quantum...

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Signature__________________________ Name__________________________ Phys 401 – Quantum Physics - Prof. Hall Final exam - December 18th, 2010, 8 am to 10 am. Show all of your work. Answers with no explanation will not receive full credit. Write your answers in the space provided on this exam. If you run out of space on a page, you may continue on a separate piece of paper. You may not use any study aides except for the given formula sheet. No calculators or communication devices are allowed. The university honor code is in effect, and your signature above indicates that you will follow it.
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1) Short answer (three points each). a) Let represent some arbitrary state of a quantum system. We decide to perform a measurement of observable A on the system. True or False : after the measurement of A, the system is left in the state A ˆ , where A ˆ is the operator associated with the observable. (Explain your answer.) b) A plane wave with energy E is incident upon a square barrier from the left, as shown in the diagram below. The wavelength of the wave on the right side of the barrier is the same as, smaller than, or larger than the wavelength on the left. (Explain your answer.)
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c) A particle-in-a-box is in a superposition of two energy eigenstates. Is the wavefunction for this system a solution of the time-independent Schroedinger Equation? (Explain your answer.) d) True or False: If we change the potential function V(x) for a system, then the eigenstates of position, momentum, and energy will change. (Explain your answer.)
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2) (three points each) Suppose we have two systems, one an infinite square well, and one
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This note was uploaded on 12/29/2011 for the course PHYSICS 401 taught by Professor Hall during the Fall '11 term at Maryland.

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FinalExam-Fall2010 - Signature_ Name_ Phys 401 Quantum...

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