ps04 - Homework (4) for Physics 316, Modern Physics I

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Unformatted text preview: Homework (4) for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault) Due Date: Friday, 02/18/05 - 9:05 in 132 Rockefeller Hall Exercise 1: Show that whenever a solution (x, t) of the time-dependent Schrdinger equation sepao rates into a product (x, t) = F (x) G(t), then F (x) must satisfy the corresponding time-independent E Schrdinger equation for some energy E and G(t) must be proportional to e -i t . o Exercise 2: A particle is in a stationary state in the potential V1 (x). How do the quantized energies for V1 (x) differ from those for a potential V2 (x) = V1 (x) + V0 that is larger over all x by a constant value V0 . Show that the spatial wave functions agree for the two potentials, except for an arbitrary complex phase. Exercise 3: In the following figures the probability distributions for the five bound states of a potential are drawn together with the energy levels. Draw the wave function of these bound states and show which qualitative features of the wave functions could have been predicted without calculation. Exercise 4: Discuss the stationary states of the potentials in exercise 3-15 of [1]. Exercise 5: Read [1,Section 4] [1] An Introduction to Quantum Physics, French and Taylor, Norton, W. W. & Company, Inc. (1990) ...
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