Developed by Jamie Lombardi (jlombard@alleg.edu), Physics Department, Allegheny College, Meadville, PA 16335.
Category: Physics (Quantum Mechanics)
"Wells" examines the wave functions of a particle in a multiple square well potential. The user determines the details of the potential by setting the number of wells, the well depth (in energy units) and the separation to width ratio in the "Square Well Parameters" window.
In the main "Function Window," the energy of the state can be adjusted using sliders. "Make Slider Finer" and "Make Slider Coarser" buttons allows the user to adjust the energy to any desired value. Alternatively, the user can type the energy in the appropriate text field.
The program numerically integrates Schrödinger's equation using the energy and potential which the user specifies. Since not all energies are eigenvalues, the displayed function will not always converge to the axis on the right of the screen. When it does, however, an eigenfunction (or valid wavefunction) has been found. In this manner the user can find the various eigenvalues and eigenfunctions of the potential.
Pressing the "Review Eigenvalues" button in the main window displays the spectrum for the eigenvalues which have already been found for that potential.
Pressing the "Examine Energy Spectrum" button in the "Square Well Parameters" window displays a good approximation to the energy spectrum. This allows examination of the band structure, degeneracy and splitting of spectral lines.
Questions concerning the main points of this program can be displayed by choosing the "Questions..." menu item. The user can save answers in a notebook which can be opened under the "Answers" submenu.
"Well" is used in Quantum Mechanics and Quantum Chemistry at Allegheny College to help students learn about eigenfunctions, eigenvalues and energy spectrums.
This application was developed under NeXTstep release 2.2.
