Shrödinger's Wave Equation in One Dimension


Middlebury College 1999
M. Benjamin, S. Chisdes, C. Tan, M. Sontum and S. Sontum
Middlebury Vermont 05753

Shrödinger's Equation

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):

  1. Select a potential V(x) from the Potential menu
  2. 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
  3. 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.
  4. Save the results using the Save menu
  5. 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


Program Discription Schrödinger's Equation Atomic Units Numerical Method



General Square Well Infinite Square Well Finite Square Well Tunneling Square Well



Harmonic Oscillator Harmonic Morse Potential Rigid Rotor Potential Hydrogen Atom Potential



Normalization Average Expectation Values Postulates References


Questions or Comments may be mailed to sontum@middlebury.edu