Return to Section 1 (Initialize)
Section 2 (Initialize)
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 Y^{2}(x). Observe and compare these results to Section 1, Problem 4.
The "parity" of a wave function is defined to be:
even if Y(x)
= Y(-x)
and odd
if Y(x)
= - Y(-x).
Display
Y(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?
Display xY^{2}(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?
Display x^{2}Y^{2}(x). The uncertainty in the operator x is <x>^{2} - <x^{2}>. 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.