Particles trapped in a box are characterized by motion in a constant potential. The electron is free to move within the box but can not leave the box. The square well provides a good model for pi electrons in conjugated polyenes like decapentaene. Here the electron is free to move along the carbon backbone but can not escape the ends of the molecule.

Schrödinger's equation for motion in a constant potential V is:

which has a general solution of:

In regions where V < E, k is purely imaginary and the solution becomes a wave:

In regions where V > E, k is real and the solution becomes an exponentially decreasing function:

The boundary conditions of the wavefunction determine the allowed energies of the trapped electron.