Infinite square well

qpcrib Particle in a box is a situation in which a particle is in a “box” that is defined by having infinite potential on both sides.

The wave function for the infinite square well is given by the following:

$${\psi }_n=\sqrt{\frac{2}{L}}\sin \left(\frac{n\pi x}{L}\right)$$

with corresponding Quantum Energy Levels given by

$$E_n=\frac{n^2{\pi }^2{\hslash }^2}{2m{L}^2}$$

Probabilities of a specific energy are given by the Fourier Coefficient and work out to the following:

$$\int {\phi }_n^{\ast }(x)\Psi (x,0)dx=c_n$$

and probability is $|c_n{|}^2$.