# Wave function/Infinite square well confusion

1. Dec 8, 2008

### Salviati

1. The problem statement, all variables and given/known data
"A particle of mass m is in the ground state of a one-dimensional infinite square well with walls at x=0 and x=a.
$$\psi_1(x) =\sqrt{\frac{2}{a}}sin(\frac{\pi x}{a})$$,
E1=$$\frac{h^2\pi ^2}{2ma^2}$$*

What is the initial wave function $$\Psi(x,0)?$$

*$$h$$ is supposed to be h bar, I just couldn't find it)

2. Relevant equations

3. The attempt at a solution
My attempt: If the general solution is a superposition of all stationary states, $$\Psi(x,t)=\sum c_n\psi_ne^\frac{-iE_nt}{h}$$, at t=0, $$\Psi(x,0)=\sum c_n\psi_n$$. Also, at this time, the particle is in the ground state (n=1), so: $$\Psi(x,0)=c_1\psi_1$$. Do I assume c1=1 at this point, because the wave function "collapses" once the energy becomes known? I'm just not sure if I understand exactly what happens when the known data is given.

The solution itself is supposed to be $$\Psi(x,0)=\psi_1(x) =\sqrt{\frac{2}{a}}sin(\frac{\pi x}{a})$$.

2. Dec 8, 2008

### Avodyne

c1=1 by normalization, assuming that $$\Psi(x,t)$$ is normalized. For a more general initial state,
$$\sum_{n=1}^\infty |c_n|^2=1.$$

3. Dec 8, 2008

### turin

You are right to be confused. You cannot know the answer to this question; that is the whole idea behind boundary conditions/initial values: they are INPUTS. For a first-order differential equation (like (d/dt)psi=iHpsi), you need one input BC for each degree of freedom.

Try \hbar.

4. Dec 9, 2008

### Salviati

Thanks guys.

$$\hbar$$