Bound States

This program enables students to search for the acceptable energy states for
a potential which they have defined. Default potentials are available or the
students may sketch their own potential freehand. They may also use our
potential creation program. However, at the moment this program does not
read correctly potentials which are created and "saved" by the potential
creation program. Instead, a potential which is created must be "exported".
This problem should be solved within a few months.

Students begin this program by selecting a potential in which they are
interested. Once the potential has been selected they may look for
acceptable energy states by hand or by using an automatic search built into
the program. When using the manual method the students select an energy and
the computer creates the wave function for that energy. The computer does
not know anything about acceptability of wave function so it creates a wave
function for any energy which the students select. However, the wave
function will diverge if the energy is not an acceptable one. This will
become quite clear because the wave function will go off the top or bottom
of the screen on the right hand side. Thus, prior to using this program the
students must have some knowledge of what wave functions represent so that
they know when to accept or reject a wave function.

The automatic method, searches for all acceptable energy states for the
potential which has been given and displays them and their energy states on
the screen.

The recommended way to use this program is to first have the students search
manually for the wave functions in several different potentials. They select
an energy which almost always will be one which is not acceptable. They then
vary that energy until they find an acceptable energy. For first searches
they can choose an energy then choose another energy and compare the two
wave functions. If one wave function diverges while going up and the second
diverges by going down, then they know that an acceptable wave function is
somewhere in between. When they feel that they have come close to an
acceptable wave function, using the arrow key enables them to fine tune the
wave function and see how the wave function starts converging to the axis as
the energy converges to an acceptable quantized state. This approach is
particularly dramatic if one leaves previous wave functions on the screen
and watches as the diverging "tail" starts moving toward the axis.

Pedagogically, this approach is quite useful to help students understand the
reasons for quantized states and acceptable wave functions. However, once
they have this understanding, the procedure can be quite tedious. Thus, for
other potentials we use the automatic search method and then discuss the
significance of the different energy states.
