# Quantum Mechanics

1. Nov 6, 2005

### Petrucci Rocks

Hi, I hope this is the right place to ask this... it's problem I have with a homework question but I think it's just me being stupid. There must be something I'm missing.
Also I apologise this isn't typed up in proper maths font or anything like I've seen some people doing on this forum... how the hell do you do that?

It says this:

At time t=0, the wavefunction of a particle of mass m in an infinite one-dimensional square well potential between x=-L/2 and x=+L/2 is
psi(x, t=0) = sqrt(2/3)phi1(x) + sqrt(1/3)phi2(x)

where phi1(x) and phi2(x) are the normalized energy eigenfunctions of the ground and first excited states.

then the first part of the question is to write down the wave function psi(x,t) at any time t>0. How do I go about finding this? since it says "write down the wavefunction" I assume it must be something really simple that I should be able to write without actually doing any working but I have no idea how to find the wavefunction for all time having only been given it for one given time. I'm one of those rubbish people who can't figure something out if I haven't been taught how to do it first. The rest of the question is dependent on this first part so it seems quite necessary...

Last edited: Nov 6, 2005
2. Nov 6, 2005

### Tide

You'll need to solve the 1D time dependent Schrodinger equation using the given wave function as the initial condition.

3. Nov 6, 2005

### qbert

For potentials that don't depend on t we can use
seperation of variables to show:
$$\psi = \sum_n c_n \phi_n(x) e^{ -i \frac{E_n}{\hbar} t }$$
The initial conditions give you the cn.
i couldn't see if the latex generated correctly, so here it is in
plane text:
psi = SUM cn phin(x) exp(-i En t / h-bar )

4. Nov 7, 2005

### Petrucci Rocks

oh.. so you just stick exp(-iEnt/h-bar) after each term and that makes it time dependent?