One-Dimensional Gaussian Wave Packet

[KiwiBlack]

Homework Statement

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.

Homework Equations

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.

 

[vela]

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.

 

[genericusrnme]

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