Infinite SquareWell
Section 1
There are several important features to realize before
starting
this exercise.
1. The walls of the graph are hard, i.e., the potential at
the walls is always infinite.
2. It will always be possible to get a mathematical solution
to the differential equation, but the important question for the physics
community is "Does the solution have physical meaning?" Solutions
will have physical meaning if they satisfy the boundary
conditions:

u(infinity) = u(+infinity) =0

u'(infinity) = u'(+infinity) =0

u(x) and u'(x) are continuous at the sides of the wells.
3. Leftclick in the graph for graph coordinates.
Rightclick in the graph to take a snapshot of the current graph.
Leftclickdrag the mouse inside the energy level spectrum to change
energy levels and wave function of the particle.
Exercises:
Section 1 (Initialize)

What are the energies for the first 6 energy levels? What
functional dependence of the energy level on the quantum number do your
results indicate?

In order to save the computer from having to deal with very small and
very large numbers, some combination of the constants in Schroedinger's
equation has been set to 1. What is the width of the well?
(The horizontal axis is in meters.) Using this width and the
theoretical values for the energy levels of an electron in the
well, determine this scaling combination and the units of energy.

Measure the wave functions by leftclicking in the graph. Do your
measurements agree with the solutions in your text? Are they
normalized?

Display Plot: u(x)^{2}. u^{2}(x)dx is the
probability of finding the electron in the range x to x+dx.
Remember that the probability of finding the electron in the box is
1. What is the probability of finding the electron in the left
half of the box for the first 6 energy levels? For n=4, what is
the probability of finding the electron in the range from x=0.25 to
0.5? From x=0.25 to 0.875? From x=0.1 to 0.35?
Section
2 (Initialize)
The Eigenvalue Physlet was written by Cabell Fisher
and Wolfgang
Christian. This lab was prepared by Dan
Boye.
© 2000 by
PrenticeHall, Inc. A Pearson Company