- #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.