## Physics 4307

### Introduction to Quantum Mechanics Homework Assignment 6 Due Date: 2:00 p.m. on Tuesday, December 01, 2015Special Note: This homework will not be accepted any later than 3:00 p.m. on Wednesday 12/02/2015!

Make and keep a copy for yourself so that you may study it for the final.

1. Work out exercise 9.4 in your text---think first, this question should not require much computation.
2. Consider the ground state of the infinite symmetric square well of width L0 at time t=0. Assume that a wily QM professor causes the walls to suddenly undergo a symmetric expansion to a new width of L=2*L0.
1. Find the first three non-zero expansion coefficients c_n of this system in terms of the 2*L0 wide well stationary states.
2. Compute the sum of the squares of the first three non-zero expansion coefficients. What does this represent?
3. Compute the expectaton value <E> including only the first three non-zero expansion coefficients. How does this compare to the ground state energy of the particle in the original unexpanded well?
4. What would happen to the sum of the c_n squared and the expectation value of the energy if we included many more non-zero coefficients in the expansion?
5. Will the original wave function ever repeat in the new well?
3. Compute Δx and Δp using the creation and destruction operators for the SHO.
As usual, write these up in a "complete" fashion by using some well chosen words, diagrams, and graphics/plots to space out the math. Good Luck!!

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