486_HW6 - Physics 486 FA07 Homework Set 6 Due: Oct 25, 2007...

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Physics 486 FA07 Homework Set 6 Due: Oct 25, 2007 1) Half harmonic potential. At t = 0, a particle is confined in the half harmonic oscillator potential: V ( x ) = 1 2 m ω 2 x 2 , for x > 0, , for x < 0. (This represents, for example, a spring that can be stretched, but not compressed.) (a) Sketch the lowest 3 eigenstates of the particle in this potential. (b) Determine the allowed energies of a particle in the half harmonic oscillator potential. Hint: This requires careful thought, but little actual computation. (c) Assume that the particle is in the ground state of the half harmonic oscillator potential. The potential is suddenly changed to that of the full harmonic oscillator (FHO) potential. If a measurement of the energy is made, what are the possible energies that can be measured? (d) After the change, what is the probability that a measurement of the energy will yield the 1 st excited state energy of the full harmonic oscillator potential?
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This note was uploaded on 09/20/2010 for the course PHYS 486 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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486_HW6 - Physics 486 FA07 Homework Set 6 Due: Oct 25, 2007...

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