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Java applet for the probability current in the one-dimensional potential well

The solutions of the Schrödinger equation for a particle in a potential well are eigenfunctions (wave-functions) to the eigenvalue En (energy level). All possible linear combinations of those functions are also solutions of the Schrödinger equation, therefore it is a linear equation.

Within this applet one can superimpose any of the first 10 eigenfunctions (n=1 until n=10). One may observe the the dynamics due to the energy dependence of the frequency (eigenfunction of higher energy values have a higher frequency). One can change composition of the wave function with the slider on the top right (1 to 10). These numbers are always complex; whereas only the real part is shown here. They are always normalized.

The applet displays the dynamics of the probability density in green and the probability current (also known as probability flux) in yellow.

 Because only ten states are considered, all solutions are periodic; if one were to add infinitely more states the wave-packet would dissipate.

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Auxiliary Functions