QUANTUM PHYSICS

Prof.dr Ing. J.F.J. van den Brand, Department of Subatomic Physics,
Vrije Universiteit, Amsterdam, The Netherlands

This resource illustrates the scattering of a particle by a fixed potential. The information has been compiled from various sources available on the Internet, most importantly from A.Edgar (see also the paper by A. Edgar, American Journal of Physics 63, 136, 1995). Any comments should be directed to jo@nat.vu.nl.

  1. Introduction
  2. Solving Schroedinger's Equation
  3. The Initial Wavepacket
  4. The Movie Collection

1. INTRODUCTION

Many quantum mechanical phenomena can be demonstrated by simulation: the time-dependent evolution of a wavepacket describing a particle subject to various interactions may be followed in time by solving Schroedinger's equation. In what follows, you will see particle-like wavepackets colliding with fixed steps, single barriers, double and triple barriers, and multiple barriers representing the periodic potential of crystals.

2. SOLVING SCHROEDINGERS EQUATION

The method used to solve the time-dependent form of Schroedinger's equation,

Eqtn 2.1
is taken from the paper by Goldberg, Schey and Schwartz (American Journal of Physics 35, pp177-186, 1966). To simplify the computations, they choose a system of units in which the particle mass is 1/2 and "h bar" (Planck's constant/2*pi) is one. If it is desired to relate the solutions described here to real particles and potentials, the conversion factors for time and distance are given in the paper by A. Edgar, American Journal of Physics 63, 136, 1995.

The movies shown here were generated by using a compiled QUICKBASIC program called "Schroedinger" to compute the wavefunctions and then reading psi psi* into Excel version V, which has an elementary and poorly-documented movie-making capability. Some notes are available describing the process for Excel V. A listing of the QUICKBASIC program "Schroedinger" is also available..
 
 

3. THE INITIAL WAVEPACKET

For each movie, the initial wavepacket is the product of a plane wave with a gaussian function which is centered at x=-0.25 at the start of the movie.
 
 

4. THE MOVIE COLLECTION

  1. The Free Particle
  2. The Potential Step
  3. The Potential Barrier
  4. Single and Multi-Well Systems
  5. The Periodic Potential
Comments etc to : jo@nat.vu.nl