Question

Use the properties of waves to explain why a particle in a rigid box can have only certain energies but not others.

Answer 1

The wave function must be finite, single valued, and must be continous. The wave function allow energy calculations using Schrodinger wave equation.

At the boundaries; the wave function inside the box must go to zero. It is continous with wave function outside the box. These boundary conditions produces a solution to schrodinger wave equation for only centains values of energies. Hence, certain energies are allowable, when we consider a particle situated in a rigid box.