Why we cannot solve quantum sho directly by fro envious series.

[wowowo2006]

I have just learned the quantum harmonic oscillator
When we start to Solve the Schrödinger equation. y"= (K - x^2) y
We look at large x behaviour and use a substitution y = u(x)* exp(-x^2 /2)
to approximate the large x behaviour first,
then we use series method to solve the equation which is in terms of u(x)

I wonder if we can use power series or froenvious series to solve the equation at the very beginning

 

[Simon Bridge]

If you don't believe your teachers or the textbook authors, there is no reason for you to believe us.
You only have one option remaining: try it and see ;)