Shrödinger's Wave Equation in One Dimension
Middlebury College 1999
M. Benjamin, S. Chisdes, C. Tan, M. Sontum and S. Sontum
Middlebury Vermont 05753
This applet is intended to be used in undergraduate physical chemistry courses to help introduce the concepts of quantum chemistry. The program numerically solves Shrödinger's time-independent wave equation for various one-dimensional potential functions V(x) that are of
chemical importance. To find the wavefunction Y(x):
- Select a potential V(x) from the Potential menu
- Enter boundary conditions and initial conditions in the data boxes to the right
- Note: all entered values must be in atomic units.
- Use "Reset Variables" to get default initial conditions
- Solve the differential equation numerically by sliding the eigen scroll bar on the far right.
- The value of the eigen value E will change the curvature of the wavefunction
Y(x) and must be varied until the set boundary conditions are
satisfied. Normally you slide the eigen value until the wavefunction becomes zero on the ends.
- Lock in on a precise eigen value using the satisfy boundary conditions button.
- Save the results using the Save menu
- Finally, graph and calculate properties of the saved wave functions
For detailed instructions see the program description in the Help menu after the applet.
Program Help
Questions or Comments may be mailed to
sontum@middlebury.edu