Below you find a summary of the solutions that we will numerically discover in our first example: The particle in a box.

This example is characterized by the potential V that is zero inside a certain region (between 0 and a) and that is infinitely large elsewhere. This imposes very important boundary conditions for the wave function phi: It must be zero in the outside region of the box.

We have solved the stationary Schrdinger equation with these boundary conditions in mind and the only valid solutions are shown below. In my other course we will derive these solutions also analytically.