The time-dependent Schrodinger equation with open boundaries

by Cemal Yalabik, Bilkent University, Physics Department. April 1998

This applet was generated from our research programs (written in fortran - of course) which we use to study electron transport properties in small geometries. It has been vastly simplified, but it still runs very slow on a not-so-fast machine.

This applet shows you a computer simulation of the time development of the wavefunction of a particle moving in an arbitrary potential. When the applet starts, you should be seeing the potential (in red) corresponding to two barriers at the bottom of the page. At the top, you will be seeing a Gaussian wave-packet (real part in green, imaginary in yellow, and amplitude in white) that is moving in this potential. You can modify the potential by moving the cursor to the area where the potential has been plotted at the bottom, and "drawing" in your modifications with the left mouse button down. (The reset button will recover the original potential.)

You also have the choice of changing the type of the wave to one that is being injected (with constant wave-number) from the left, by clicking on the second button. On "slow" machines, wait until you see the effect of a mouse event (such as clicking a button or plotting in a modification for the potential) before you attempt a second mouse event.

Things to watch:

Technical details in:

"A numerical implementation of absorbing and injecting boundary conditions for the time-dependent Schrodinger equation"
M. C. Yalabik, M. Ihsan Ecemis, Phys. Rev. B51, 2082 (1995).