# Potential Barrier help starting problem

1. Dec 5, 2012

### jahaition

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

Infinite Potential Barrier
particle moving in one dimension is incident upon a potential barrier given by V (x) = Gδ(x) where δ(x) is the Dirac delta function and G is a constant with units of energy times distance. (The delta function must have units of inverse distance because its integral is unity.)

1. Solve the time independent Schrodinger equation to find the wavefunctions uE(x) in the two regions x < 0 and x > 0. Be sure to define all your variables.

2.Write down (but do not yet solve) the two matching conditions at x = 0 in terms of the various wavefunction amplitudes

3.Solve the two equations and find the reflection and transmission coefficients for the barrier in terms of the energy of particle and the constant G.

2. Relevant equations

3. The attempt at a solution

1. U=Ae^ikx + Be^-ikx, x<0
U=Ce^kx + De^-kx, x>0

Last edited by a moderator: Dec 6, 2012
2. Dec 6, 2012

### vela

Staff Emeritus
Your solution for x>0 isn't correct.

You need to put a bit more effort into working problems on your own before you can receive help here.

3. Dec 6, 2012

### andrien

write down schrodinger eqn and integrate it so as to find a condition between the coefficients,you used while defining the U's.(you have forgotten i somewhere)

4. Dec 6, 2012

### jahaition

-h^2/2m (ψ'') + V(u)=Eu

I. x<0
ψ''+(2m/h)E=0
K^2=2mE/h

ψ=Ae^ikx +Be^-ikx

II. x>0
ψ''+(2m/h)(Gδ(x)-E)=0
K^2=(2m/h)(Gδ(x)-E)

ψ=Ce^kx +Be^-kx => ψ=Be^-kx

This what i got, did i make a mistake somewhere?

5. Dec 6, 2012

### vela

Staff Emeritus
Yes, for starters, what is u? Is it your independent variable, as suggested by your writing V(u)? If so, then what's x supposed to be? Why doesn't it show up in your subsequent work?

Why did you include the delta function for x>0 but not x<0? Should it be there for x<0, or should it not be there for x>0?