Harmonic oscillator

1. Nov 16, 2005

Sojourner01

Ok, fairly basic quantum mechanics assignment.

One question deals with (I think) the coefficients of the Hermite polynomial. Unfortunately, the lecturer hasn't told us anything about this method, so I donn't know what it's called or what the point of it is, and it's not in any of the examples of Hermite polynomials I can find.

I have the summation:

$$\\sum_{n=-\\infty}^\\infty [(k+2)(k+1)c_{k+2} + (2 \\epsilon -2k -1)c_{k}] y^k = 0$$

Show that the above implies that the coefficients for each power of y are themselves zero, by considering the derivatives of [] evaluated at y=0?

It'd be nice if I knew what these damn numbers were. It'd be even nicer if I knew what this was called so I could look it up.

edit: well, I can't get the LaTex to display what I want, but I hope you get the idea...

Last edited: Nov 16, 2005
2. Nov 16, 2005

Galileo

Use a single backslash before LaTeX command:
$$\sum_{n=-\infty}^\infty [(k+2)(k+1)c_{k+2} + (2 \epsilon -2k -1)c_{k}] y^k = 0$$