- #1

E92M3

- 68

- 0

## Homework Statement

[tex]\psi(x,0)=Ae^{-ax^2}[/tex]

Normalize and find:

[tex]\psi(x,t)[/tex]

## Homework Equations

[tex]1=\int_{-\infty}^\infty\psi^*\psi dx[/tex]

## The Attempt at a Solution

[tex]1=A^2\int_{-\infty}^\infty e^{-2ax^2} dx[/tex]

let:

[tex]u=x\sqrt{2a}[/tex]

[tex]1=A^2\frac{1}{\sqrt{2a}}\int_{-\infty}^\inftye^{-u^2} du=A^2\sqrt{\frac{\pi}{2a}}[/tex]

Therefore:

[tex] A=(\frac{2a}{\pi})^{1/4}[/tex]

[tex]\psi(x,t)=(\frac{2a}{\pi})^{1/4}e^{-2ax^2-i\frac{\hbar k}{2m}t}[/tex]

This is too simple to be the right answer. I think I'm missing the point of the question. Please point me to the right direction.