Homework Help: Finding potential for a given wave function

1. Sep 18, 2008

Desh627

Here's the sitch:

I am given an equation, A*e-a(mx2/h-bar+it)

I need to find the value for A that will satisfy normalization, as well as find the Potential of the Schrödinger Equation using this value.

What do I do?

P.S. I have NOT learned gaussian integration, which is where I run into my first major problem, and this stops me from completing the problem.

Thanks guys,
Desh627

2. Sep 18, 2008

Desh627

I should also mention what I have solved so far...

psi (x,t) = A*e-a(mx2/h-bar+it)

psi (x,0) = A*e-a(mx2/h-bar+i(0))
psi (x,0) = A*e-a(mx2/h-bar)

Integral from negative infinity to infinity dx (absolute value)A*e-a(mx2/h-bar)(/absolute value)2 = 1

A2 Integral from negative infinity to infinity dx e-a(mx2/h-bar)=1

A = sq. rt (1/Integral from negative infinity to infinity dx e-a(mx2/h-bar))

and this is where I run out of room.

I should also mention that I have taken high school physics and ap calc, but no linear algebra or anything beyond ap calc.

3. Sep 19, 2008

yaychemistry

Hi,
Let's see if we can't figure this one out.
To figure out how to normalize your wavefunction, you need to know what the integral of a Gaussian function is, where a Gaussian function is any function of the form:
$$f\left(x\right) = \exp\left(-\frac{x^2}{2\sigma^2}\right)$$
I doubt you would know a good technique from AP calculus to solve this integral, so I would suggest reading this wikipedia article:
http://en.wikipedia.org/wiki/Gaussian_integral

For the second part, since your wavefunction already has time explicity in it, we can make a guess that it's a solution to the time dependent schrodinger equation:

$$\hat{H}\psi = i\hbar\frac{\partial}{\partial t}\psi$$

where H is the operator such that:
$$\hat{H}\psi\left(x\right) = -\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\psi\left(x\right) + V\left(x\right)\psi\left(x\right)$$
And V(x) is the potential. Try applying the time-dependent schrodinger equation and see if you can convert the problem into a differential equation in x only (and not t). From there it might be possible to figure out what V(x) is.

Last edited: Sep 19, 2008