Hi guys, this assignment is driving me nuts! Thank you very much for the help!!(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Consider the infinite square well described by V=0, -a/2<x<a/x, and V=infinity otherwise. At t=0, the system is given by the equation

[tex]\Psi(x,0) = C_{1} \Psi_{1}(x) + C_{2} \Psi_{2}(x)[/tex]

[tex]\Psi(x,0) = \frac{1}{\sqrt{2}} \sqrt{\frac{2}{a}}cos\left \frac{\pi x}{a} \right + \frac{1}{\sqrt{2}} \sqrt{\frac{2}{a}}sin\left \frac{2 \pi x}{a} \right[/tex]

(a) Obtain [tex]\Psi (x,t)[/tex]

(b) Use this [tex]\Psi (x,t)[/tex] to calculate <H>, delta H, <x> and <p>.

(c) What can you say about the result you obtained from part (b). Explain.

2. Relevant equations

[tex]\psi(x,0)=\sum_{n=1}^{\infty}c_n\psi_n(x)[/tex]

[tex] \psi_{n}(x)= \sqrt{\frac{2}{a}}sin\left \frac{n \pi x}{a} \right[/tex]

[tex]E_{n}=\frac{n^2\pi^2\hbar^2}{2ma^2}[/tex]

[tex]c_{n}=\int_{0}^{a} \sqrt{\frac{2}{a}}sin\left \frac{n \pi x}{a} \right \psi(x,0)dx[/tex]

3. The attempt at a solution

Um...this problem is kind of similar to the infinite well problem posted below earlier...I want to know if the formulae up there are the right one to use first...before I blindly apply it and do the integrals...

the second term in the wave function looks like an eigenfunction for the energy...but the first one is a cosine so I am not sure what to do there...do I need to...split them up?

The equations above are for the infinite well from o to a...but this question is from -a/2 to a/2...so I am not sure if the eigenfunctions [tex]\Psi(x)[/tex] change ...

I also know [tex]\Psi (x,t)[/tex]can be obtained from multiplying [tex]\Psi (x,0)[/tex]by the appropriate phase factor once the [tex]\Psi_{n} (x,0)[/tex] is written as a linear combination of the energy eigenfunctions...but then there's the cosine in the first term...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Another inifinite square well

**Physics Forums | Science Articles, Homework Help, Discussion**