The curricular material uses the QMSuperpositionApp
to show wave functions in color-as-phase representation (hbar = 2m = 1).
The position-space energy eigenstates and their energies are calculated either
numerically for any user-defined potential energy function, V(x),
or calculated analytically for the special cases of the infinite square well,
the periodic infinite well, and the simple harmonic oscillator.
The power of QMSuperpositionApp is that it allows the author or
user to specify a set of expansion coefficients for in a comma-delimited list.
The program then calculates the sum over states, and then automatically evolves
the superposition state in time. The use of analytic solutions for each
eigenstate allows the simulation to run for a long period of time and yet never
accumulate numerical error since the wave function is calculated anew at each
time step according to an analytic formula.
Depending on the analysis one wishes to perform, one of the following programs
based on QMSuperpositionApp (which itself only shows the
position-space wave function) in the "qm" sub-package within the "Davidson
package" can be chosen:
QMSuperpositionProbabilityApp adds a view of the position-space
probability density.
QMSuperpositionExpectationXApp adds a view of the expectation value of x, <x>.
QMSuperpositionExpectationPApp adds a view of the expectation value of p, <p>.
QMSuperpositionCarpetApp adds a view of the position-space quantum carpet.
QMSuperpositionMomentumCarpetApp which adds a view of the momentum-space carpet.
QMSuperpositionFFTApp which adds a view of the momentum-space wave function.
This example shows the interactive mode for the quantum-mechanical superposition program.