Quantum physics potential well.

[arierreF]

Homework Statement

In the instant t=0, we have the following wave function of a particle in a infinite potential well with a width a.

\psi (x) = \sqrt{\frac{2}{a}}\text{Sin}\left[\frac{n*\text{Pi}*x}{a}\right]


Calculate the momentum space wave function.



Ok, i just want to confirm if i have to use the following equation to calculate momentum space wave function:

\phi (p) = \sqrt{\frac{1}{2*\text{Pi}*\hbar}}\int _0^ae^{-i*p*x/\hbar}dx\sqrt{\frac{2}{a}}\text{Sin}\left[\frac{n*\text{Pi}*x}{a}\right]


Considering that the well has a zero potential between 0 and a.

 

[vela]

Right. The momentum-space wave function is simply the Fourier transform.

 

[arierreF]

ok thanks !