Series solution for the states of the SHO

One way to derive the form for the Hermite polynomials is to solve Schrödinger's equation using a power series method. Although this is not the most elegant method, it serves to illustrate important features of the TISE. It is also important to understand this method because it may often may be applied when a more clever solution is not so apparent.

• The eigenvalue equation for the
• The eigenvalue equation for the .
• Putting the pieces together
• The growth of when the series does not terminate