Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Suppose $$\Psi (x, t=0)=Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x).$$ If $\psi _n$ are the energy eigenfunctions how would I derive $\Psi (x,t)$?

I am having trouble with the $\psi_n$ for which I don't know how to deal with when I use Fourier transform

$$\phi(k)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \left(Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x)\right)\, dx $$

Any hint would be appreciated.

share|improve this question

closed as off-topic by Colin McFaul, Brandon Enright, Chris White, DavePhD, Kyle Jun 16 at 16:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Colin McFaul, Brandon Enright, DavePhD, Kyle
If this question can be reworded to fit the rules in the help center, please edit the question.

add comment

1 Answer 1

The time dependence is given by $$ \psi(x,t) = \psi_n(x) e^{-iE_nt/\hbar}$$ where $E_n$ is the energy of the system.

share|improve this answer
1  
I would put subscript $n$ on your $\psi$s to indicate it is only valid when $\psi$ is an energy eigenfunction. –  BMS Oct 3 '13 at 18:53
    
See Griffiths' QM. Chapter 2. –  Ome Mar 12 at 17:57
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.