How to Find Psi(x,t) in an Infinite Potential Well?

[natugnaro]

Homework Statement

Hi,
Particle of mass m is found in one-dimensional infinite potential well with walls 0<=x<=a.
In t=0 the normalized wave function is:
$$\psi(x,t=0)=A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})$$

find psi(x,t)

Homework Equations

?

The Attempt at a Solution

$$\psi(x,t)=\sum C_{n} e^{\frac{-iE_{n}t}{\hbar}}\phi_{n}(x)$$

$$C_{n}=\int^{a}_{0}\phi_{n}(x)\psi(x)dx$$

$$C_{n}=\int^{a}_{0}Sin(\frac{n \pi x}{a})A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})dx$$


I could do the integral and find Cn coefficients, but it takes time.
Is there an easier way for findin psi(x,t) ?

 

[malawi_glenn]

Homework Statement

Hi,
Particle of mass m is found in one-dimensional infinite potential well with walls 0<=x<=a.
In t=0 the normalized wave function is:
$$\psi(x,t=0)=A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})$$

find psi(x,t)

Homework Equations

?

The Attempt at a Solution

$$\psi(x,t)=\sum C_{n} e^{\frac{-iE_{n}t}{\hbar}}\phi_{n}(x)$$

$$C_{n}=\int^{a}_{0}\phi_{n}(x)\psi(x)dx$$

$$C_{n}=\int^{a}_{0}Sin(\frac{n \pi x}{a})A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})dx$$


I could do the integral and find Cn coefficients, but it takes time.
Is there an easier way for findin psi(x,t) ?

I don't think so, perhaps if you use tables of standard integrals or maple / mathematica.

 

[natugnaro]

Ok, thanks.
Just wanted to make shure I'm not missing something.

 

[malawi_glenn]

Ok, thanks.
Just wanted to make shure I'm not missing something.

there is standard integrals for ortonogal cos and sin integrals, if you want more hints.