# Undergrad w/o formal quantum introduction, having trouble

1. Jul 27, 2012

### agm2010

I am about to start my junior-level courses (advanced mechanics, quantum I, etc) and I've been working on a project with a professor this summer. Basically, I am trying to reproduce the results of this paper: http://arxiv.org/abs/nucl-th/9611049 . Right now I am trying to work only with 1-dimensional quantum oscillators, and will later apply it to 2 and 3-body systems.

This has been tricky as I only have a very basic sophomore-level knowledge of quantum material, so I'm trying to simultaneously learn basic quantum topics while working on the problem.

At this point, I'm working with this:

ψ$_n$(x)=N$_n$H$_n$(αx)
ψ$_m$(x)=N$_m$H$_m$(αx)

$\int$ ψ$_n$(x)ψ$_m$(x) dx = <n|m> = 0

Where H is a hermite polynomial, and N is a proportionality constant. I need to find the n and m that make the last statement true. I have a feeling this should be trivial, but keep getting stuck. My professor said this would be a good job for Mathematica/Maple, so I'm hoping someone can guide me in the right direction with that calculation. Is there a good resource for dealing with problems of this type in Maple? Also, I have been using Griffiths...is that the best quantum introduction?

Thank you

Edit: Maybe the homework forum is more appropriate? Sorry

Last edited: Jul 27, 2012
2. Jul 27, 2012

### fzero

The Hermite polynomials are orthogonal with respect to a Gaussian weight:

$$\int_{-\infty}^\infty H_n(x) H_m(x) e^{-x^2} dx = 0~~~(m\neq n).$$

Are you sure that your wavefunctions are not $\psi_n(x) = N_n H_n(ax) e^{-a^2 x^2/2}$?

Griffiths is a decent QM book for an undergrad. A recent discussion of it is in this thread.