## Physics 4307

### Introduction to Quantum Mechanics

Homework Assignment 6

Due Date: 2:00 p.m. on Tuesday, December 01, 2015

**Special 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.

- Work out exercise 9.4 in your text---think first, this question should not
require much computation.
- 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.
- Find the first three non-zero expansion coefficients c_n of this
system in terms of the 2*L0 wide well stationary states.
- Compute the sum of the squares of the first three non-zero expansion
coefficients. What does this represent?
- 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?
- 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?
- Will the original wave function ever repeat in the new well?

- 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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