The standing wave formed for a particle trapped within a box is analogous to the standing wave formed on a string stretched between two rigid supports. It can thus be deduced that the wave function ψ_{n}(x) of this particle has the same form as the displacement function y_{n}(x) for the standing wave on a string stretched between the two rigid supports.

$\psi_{n} \left( x \right) = A sin \left( \frac{n \pi}{L} \right) x$

For a particle trapped within a box, U = 0 inside the box, and the general time-independent Schrodinger equation becomes

$- \frac{h^{2}}{2m} \frac{d^{2} \psi}{dx^{2}} = E \psi$