# One-Dimensional Gaussian Wave Packet

1. Feb 7, 2012

### KiwiBlack

1. The problem statement, all variables and given/known data
Consider a one-dimensional wave packet with $\phi$(p) = A $\Theta$ ((h/2$\pi$) / d -|p-p0|)

Determine the constant A and find the spatial wave function ψ(x). Ignore temporal evolution.

2. Relevant equations

3. The attempt at a solution
Honestly this is a little embarrassing, but the only thing I really need to know is what $\Theta$ is. Is it a constant, or shorthand for e^? If I know that, I should be good. I can't find any info in my notes.

Last edited: Feb 7, 2012
2. Feb 7, 2012

### vela

Staff Emeritus
I'm not familiar with that notation at all. A Gaussian has the form
$$e^{-\frac{(p-p_0)^2}{2\sigma^2}}$$where p0 is the average and σ is the characteristic width.

3. Feb 7, 2012

### genericusrnme

Never before have I seen that notation...
Usually the capital phi or psi are linear combinations of the little phi/psi's...