Maple plots for particles in square wells


Probability densities for various stationary states of a particle confined to a finite interval in one dimension.

particle in box, n=2
particle in box, n=3
particle in box, n=10
 

The above plots can be produced with the MAPLE commands like the following

> restart;

> with(plots);

> with(plottools);

> plot( 1 - cos(2*3*x), x=0..Pi, y=0..2.2, axes=BOXED, title="probability density n=3" );


Probability density for the non-stationary state of a particle in a one dimensional box in Question 3 of Sheet 2.

animated particle in box
 

Notice how the probability density changes like the particle bouncing back and forth in the classical picture.

This used the MAPLE "animate" command.

 

Probability densities for various stationary states of a particle confined to a square region in a plane (Question 4 of Sheet 2).

 

These plots can be produced with commands along the lines of

> plot3d( (1 - cos(2*3*x))*(1 - cos(2*2*y)), x=0..Pi, y=0..Pi, axes=BOXED, title="probability density, j=3, k=2" );

By using MAPLE you will be able to rotate the surface plots to discover more detail.

  • Applet of the time evolution of a particle in a box
  • Plots of harmonic oscillator probability densities

    Link to Mathematical Institute Home Page
    Link to Mathematics at Balliol
     
    This page was last updated
    on 30 April 2004
    by
    KC Hannabuss