Features Download Images and Screenshots Animations

The IDL program SE_SIM.PRO is an
application that provides visualization of the time-evolution of quantum
mechanical wavefunctions in 1 dimension. It is essentially a GUI wrapper
for a function, TDSE_SOLVER.PRO, that solves the Schrodinger equation for a
user-specified initial wavefunction and potential. SE_SIM.PRO requires IDL
6.2 or higher to run.

The numerical integration of the Schrodinger equation is based on an
algorithm presented in an article by Goldberg et. al. in the American Journal of
Physics in 1967. In this formulation, the Schrodinger equation is
solved with h-bar = 1 and 2m = 1. In this scaling, the units for x and m can be
selected freely but such selection determines the units of time
and energy. For instance, in one scaling, energy can be expressed in eV,
unit distance is 0.03 nm, and a unit of time is 0.66 fs (femto-seconds).

The application SE_SIM.PRO has a number of useful features listed below.

- Custom user-defined potential barriers, wells, and Gaussian wavepackets
- Full control over the simulation conditions including discretization of time and space
- Ability to design your own complicated potential systems using the mouse
- Full control over animation playback including skipping frames, pause/resume
- View time-evolution of the wavefunction (real and imaginary components), probability density, and/or probability current (j(x,t)) in position space
- View time-evolution of the wavefunction (real and imaginary components), and/or the probability density in momentum space
- Display the time-dependent integrated probability density in configuration and momentum space over a user-defined range
- Manually select any frame in the animation to display
- Save any frame in PNG graphics format
- Save animation as an animated GIF file

Example frame output from SE_SIM of a wavepacket reflecting from a step barrier.

Example image output from SE_SIM of a wavepacket scattering (transmission + reflection) from a potential well. Here the probability density is displayed.

Example image output from SE_SIM of a wavepacket propagating into a periodic potential well. The probability density is displayed.

Wavepacket tunneling through a potential barrier-P(x,t) & P(k,t)

Wavepacket incident on a double barrier-P(x,t)

Wavepacket incident on a step barrier-Real and imaginary parts of the wavefunction

Wavepacket incident on a potential well with a "lip", exciting a metastable state of the well-Real and imaginary parts of the wavefunction

(updated 07/14/07)