Particle in a Box: Find Potential Energy U of x

[cscott]

Homework Statement

In a region of space, a particle with zero total energy has a wave function
$$\Psi (x) = Axe^{-x^2/L^2}$$

Find the potential energy U as a function of x.

The Attempt at a Solution

I don't understand how this particle can have zero total energy? Wouldn't this imply that the potential energy is simple 0 everywhere...

 

[cscott]

Wait, would I have to describe the potential like we do for an infinite square well?

 

[christianjb]

Use time-independent Schrödinger eqn.

Zero total energy means that PE=-KE.

 

[cscott]

So with E = 0 I can say $$\frac{d^2\Psi}{dx^2} = -\frac{2mU}{\hbar ^2} \Psi$$

which mean I can get solutions just like in my text but I don't what I can apply as boundary conditions or how to get U in terms in x.

 

[christianjb]

Divide both sides by psi(x) to get U(x).

psi(x) already obeys the relevant boundary conditions.

 

[cscott]

Ah I see now :P I feel kind of stupid :\

Thanks!

 

[giffary]

thanks!

 

[andromeda2008]

i would lke to b informed how to prepare a lab report on the Hall Effect hopping that i will b given an intensive help over the matter
N.B...i did the experment of the hall effect when a moving conducter moves through a magnetic fild while two variable resistors of 8 and 16 ohms connected to it and the source and the ammeters so as to had the observation
hopping that i will b directed sufficently
urs faithfully......