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QMWave Applet




Instructions

The applet below is divided into four panels: Potential Generator, Energy Solutions, Probability Density, and Energy Selector. Typical usage is as follows:

  1. Use sliders in the Potential Generator panel to specify the potential landscape seen by the particle.
    • The potential landscape will consist of a series of equally sized rectangular potential barriers separated by regions of zero potential called wells.
    • Well Width - is the width in spacial units of each individual well (the empty spaces between barriers).
    • No. of Barriers - is the number of rectangular potential barriers that will exist in the potential landscape.
      Warning: setting this number larger than 8 can slow down calculations significantly - it is still reasonable to do this in order to see the energy levels, but subsequently choosing an energy level to view the probability density can be prohibitively slow.
    • Barrier Width - is the length of one of each individual barrier in 1D space (recall that the model under consideration is one-dimensional).
    • Barrier Height - is the "height" in units of energy of each individual potential barrier.
    • Once you have adjusted the sliders to create the potential you are interested in, click on the Go button in the Potential Generator panel.

  2. At this point there should be a series of horizontal lines appearing in the Energy Solutions panel as well as a diagram of the potential barriers displayed in the Probability Density panel.
    • The vertical axis in both the Energy Solutions panel and the Probability Density panel are in units of energy and are to scale with one another.
    • The horizontal lines in the Energy Solutions panel correspond to allowed energy levels - clicking on one of the horizontal lines in the Energy Solutions panel will then display the spacial probability density for a particle at that energy.
    • The buttons in these two panels can be used to navigate the graphs being displayed, however the reset buttons are "buggy" so I don't advise using them.







QMWave

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