## Infinite Square-Well  Section 2

 Plot: u(x) Plot: u(x)2 Plot: x*u2(x) Plot: x2* u2(x)

Section 2 (Initialize)

1. Note where x = 0 and the wall edges are located in comparison to the infinite square-well solution in Section 6-5 of your text.  How does this difference affect the energy levels and/or the wave functions?  Explain.  Display u2(x).  Observe the n = 4 level and compare these results to Section 1, Problem 4.

2. The "parity" of a wave function is defined to be:
even    if   u(x) = u(-x)    and    odd     if    u(x) = - u(-x).
Display
u(x).  What is the parity of each of the wave functions for the first 6 energy levels?  What general conclusion can you draw regarding the quantum number and the parity for an arbitrary energy level?

3. Display x u2(x).  The integral, or the area under the curve, of this function from x= -0.5 to 0.5 is the expectation value of the position operator x.  The expectation value is interpreted as the average value of x after many measurements.  Positive areas are denoted by the blue fill and negative areas by the yellow fill.  What are the expectation values of x for the first 6 energy levels?  Explain your result.  Return to Section 1.  In Section 1, what are the expectation values of x for the first 6 energy levels?  Why are they different from your Section 2 results?

4. Display x2u2(x).  The uncertainty in the operator x is the square root of |<x>2 - <x2>|.  From the previous problem, what is <x>2?  Is the uncertainty in the position operator nonzero?  Are the eigenfunctions of the energy also eigenfunctions of the position operator?

The Eigenvalue Physlet was written by Cabell Fisher and  Wolfgang Christian.  This lab was prepared by Dan Boye.

© 2000 by Prentice-Hall, Inc. A Pearson Company