Infinite square well eignefunctions

[stunner5000pt]

Homework Statement

The eignefunctions for a infinite square well potential are of the form

$$\psi_n} (x) = \sqrt{\frac{2}{a}} \sin \frac{n\pi x}{a}.$$

Suppose a particle in this potnetial has an initial normalized wavefunction of the form
$$\Psi(x,0)= A\left(\sin \frac{\pi x}{a}\right)^5$$

What is the form of $Psi(x,t)$

2. The attempt at a solution
Now the given wavefunction $Psi(x,0)$ can be made to fit the infinite square well by making it a superposition

$$\Psi(x,t) = \sum_{n=1} c_{n} \psi_{n} (x) e^{iE_{n}t/\hbar}$$

is that it?

it cnat be that simple...

thanks for your advice

 

[nrqed]

Homework Statement

The eignefunctions for a infinite square well potential are of the form

$$\psi_n} (x) = \sqrt{\frac{2}{a}} \sin \frac{n\pi x}{a}.$$

Suppose a particle in this potnetial has an initial normalized wavefunction of the form
$$\Psi(x,0)= A\left(\sin \frac{\pi x}{a}\right)^5$$

What is the form of $Psi(x,t)$

2. The attempt at a solution
Now the given wavefunction $Psi(x,0)$ can be made to fit the infinite square well by making it a superposition

$$\Psi(x,t) = \sum_{n=1} c_{n} \psi_{n} (x) e^{iE_{n}t/\hbar}$$

is that it?

it cnat be that simple...

thanks for your advice

yes. Just use a table of trig identities to write sin to the fifth power as a sum of sine functions of different arguments. That will directly give you the expansion in terms of the eigenstates of the Hamiltonian.

patrick