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