How Do You Normalize a Quantum Wavefunction in One Dimension?

[czaroffishies]

I am very sorry that I did not use latex here. It didn't seem to be functioning properly, but I tried to make this readable.

Homework Statement

The wave function for a particle moving in one dimension is

Psi(x, t) = A x e^[-(sqrt(km)/2(hbar))*x^2] e^[-i*sqrt(k/m)*(3/2)*t]

Normalize this wave function.

Homework Equations

Psi(x,t)^2 = probability that particle is found at point x.
So, total probability of particle being found anywhere is integral from -inf to +inf of Psi*(x, t)*Psi(x,t) dx, where Psi*(x, t) is the complex conjugate of Psi(x, t), and must be equal to 1.

The Attempt at a Solution

First multiplied Psi(x, t) by complex conjugate:

Psi*(x, t) * Psi(x, t) =

(A x e^[-(sqrt(km)/2(hbar))*x^2] e^[i*sqrt(k/m)*(3/2)*t]) times
(A x e^[-(sqrt(km)/2(hbar))*x^2] e^[-i*sqrt(k/m)*(3/2)*t])

= A^2 x^2 e^2*[-(sqrt(km)/2(hbar))*x^2]

= A^2 x^2 e^[-(sqrt(km)/(hbar))*x^2]

This is somewhat embarrassing, but I am not sure I know how to integrate this. And if it can't be integrated by normal means, it probably wouldn't show up as the first problem in an introductory quantum mechanics book.

I'm not seeing where I went wrong... any help is appreciated!

 

[Eynstone]

It's a standard gaussian integral.

 

[czaroffishies]

Sweet, thanks.

 

[Feldoh]

http://en.wikipedia.org/wiki/Lists_...integrals_lacking_closed-form_antiderivatives

Should be of some help