Skip to main content

Illustration Energies of an Electron with Symmetric Wave Function in the Finite Potential Box (Graph)

Energies of an Electron with Symmetric Wave Function in the Finite Potential Box (Graph)
Get illustration

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Sharing and adapting of the illustration is allowed with indication of the link to the illustration.

Graph of the following transcendental equation:$$ \tan\left( \frac{L}{2}\sqrt{\frac{2m}{\hbar^2} \, W^+} \right) ~=~ \sqrt{\frac{V_0}{W^+} ~-~ 1} $$

Here, the right and left sides of the equation were plotted (a bit rescaled) separately as a function of \(W^+\). This equation was obtained by solving the Schrödinger equation for an electron in a finite potential well described by a symmetric wave function. Und \(W^+\) entspricht der Energie des Elektrons. The intersections \(W^+_1 \) and \(W^+_2\) are allowed energies of the electron within the potential box. In this case the electron can occupy only two energies in the potential box if it has a symmetric state.