HW #5 - outcomes and their probabilities? c) Now assume...

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Physics 591 - Homework Set # 5 Due: Monday, September 28 5 pm 1. In class we considered the problem of a particle of mass m that is conFned to exist on a circular ring of circumference a. We solved the eigenvalue problem for this, and our solution in class can be the starting point for this problem. Assume that at time t=0 the particle has an energy the ring suddenly expands to a circumference of 3a (triple its original length). a) ±ind the uncertainty in the energy of the particle right after the expansion of the ring. Do this by explicitly computing and ignoring discontinuities when taking the derivatives. b) If the energy is measured immediately after the expansion of the ring, what are the possible
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Unformatted text preview: outcomes and their probabilities? c) Now assume that the particle is conFned to one third of the ring by the potential ind the wavefunction and energy of the new ground state. The next problem must be done ``by hand''; that is, without aid from a computer program such as Mathematica, Maple, etc. 2. Consider a particle whose wave function is a vector in a . A certain operator in the space is given in matrix form in what we will call ``basis 1'' by the matrix A measurement of is made. If the initial state was a) Write down the density matrix describing the ensemble that results after the measurement of in the basis in which is diagonal b) What is the probability of obtaining the result...
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This note was uploaded on 02/24/2011 for the course PHYS 591 taught by Professor Valenc during the Fall '09 term at Iowa State.

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HW #5 - outcomes and their probabilities? c) Now assume...

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