# Homework Help: Quantum Mechanics Particle moving in 1-D potential

1. Mar 15, 2012

### 20930997

1. The problem statement, all variables and given/known data
I've been attempting this one for a while now and so far it has been to no avail. The question itself is in the attached document.

I am given an expression that defines the wavefunction moving in 1-D over an interval and the time component is fixed with t=0.

2. Relevant equations

〖|ψ(x,0)|〗^2 = prob dist, in which likelihood of finding a particle at that point can be inferred.

3. The attempt at a solution

first of all I assume that (A) is a complex constant and as a result i multiply the wavefunction by its conjugate to get the following,

〖|ψ(x,0)|〗^2=|A|^2 (x^4-2x^3 a+x^2 a^2) which im not sure is correct and furthermore have no idea how to sketch it.

any guidance would be appreciated!

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2. Mar 15, 2012

### vela

Staff Emeritus
That's correct, but it would probably be better not to multiply it out initially. Just leave it as
$$|\Psi(x,0)|^2 = \begin{cases} |A|^2 (x-a)^2 x^2 & 0 \le x \le a \\ 0 & \text{otherwise} \end{cases}$$ Surely, you must have done curve sketching in algebra and calculus. Where does the function vanish? Where is it positive? Where is it negative? Where does it attain a maximum or a minimum?

3. Mar 15, 2012

### 20930997

ahh yes that makes it alot clearer, thanks for the help!

4. Mar 16, 2012

### 20930997

I'm also having difficulty with part b of this question.

I tried using a symmetry approach to try and deduce the value of |A| but in my working the |A|^2 term ends up being cancelled which is of no use to me.

again any pointers would be much appreciated.

5. Mar 16, 2012

### vela

Staff Emeritus
You need to use the normalization condition to determine |A|.