Integral of a Hermitian squared?

[maroon]

1. The problem statement, all variables and given known data

Compute: ∫x²(H_n(x))²e^-x2dx

The boundaries of the integral are -∞ to +∞

Homework Equations

By Rodrigues' formula:

H_n(x) = (-1)ⁿe^x2dⁿ/dxⁿ(e^-x2)

The Attempt at a Solution

I proceed to plug in my expression for H into the integral, however, I'm insure as to what happens to the dependent derivative/integral when the derivative is squared. I believe the solution to this problem is straight "plug and chug." I got stuck pretty early and don't want to proceed until i know what to do with the derivative.

Thanks in advance for your help!

 

[Dustinsfl]

The Hermitian operator is supposed to be orthonormal. However, I am not familiar with it. Since you have the Hermitian squared, the integral should be 1

 

[Dick]

The Hermitian operator is supposed to be orthonormal. However, I am not familiar with it. Since you have the Hermitian squared, the integral should be 1

The post is about Hermite polynomials, not Hermitian operators.