- #1

rkdaniels

- 4

- 0

- Homework Statement
- I am attempting to find a solution to the following problem

- Relevant Equations
- See below

I am currently stuck trying to work this out. I have an infinite potential with walls at x=0 and x=a, with the initial state:

$$

\psi(x,0) = A_2(exp(i\pi(x-a)/a)-1)

$$

I am trying to find psi(x,t). I know that

$$

A_2(exp(i\pi(x-a)/a)-1) = A_2(-exp(i\pi/a)-1)

$$

And this enables me to find the normalization constant:

$$

A_2 = \frac{1}{\sqrt{a}}

$$

I also know that I can expand psi(x,0) as:

$$

\psi=\sum c_n\phi_n

$$

where

$$c_n = \langle\phi_n|\psi\rangle$$

and

$$\phi_n = \sqrt{\frac{2}{a}}\sin\left( \frac{n\pi x}{a} \right)$$

I get stuck trying to find the coefficients here. When I try to integrate, I end up with something quite horrific and I'm sure it should be relatively simple.

$$

\psi(x,0) = A_2(exp(i\pi(x-a)/a)-1)

$$

I am trying to find psi(x,t). I know that

$$

A_2(exp(i\pi(x-a)/a)-1) = A_2(-exp(i\pi/a)-1)

$$

And this enables me to find the normalization constant:

$$

A_2 = \frac{1}{\sqrt{a}}

$$

I also know that I can expand psi(x,0) as:

$$

\psi=\sum c_n\phi_n

$$

where

$$c_n = \langle\phi_n|\psi\rangle$$

and

$$\phi_n = \sqrt{\frac{2}{a}}\sin\left( \frac{n\pi x}{a} \right)$$

I get stuck trying to find the coefficients here. When I try to integrate, I end up with something quite horrific and I'm sure it should be relatively simple.