# Transmission coefficient (quantum tunnelling)

1. Jul 3, 2010

### Camilla

1. The problem statement, all variables and given/known data
What is transmission probability (T), when the incident particle energy (E) is equal to the energy of the barrier (U)?

2. Relevant equations
Equations to transmission and reflection probabilities.

3. The attempt at a solution
I know that the probability isn't null and less than 1, but i don't know how to proceed when the energy of E is equal to U.

That is all the information I have, I would appreciate any help.

Last edited: Jul 4, 2010
2. Jul 4, 2010

### vela

Staff Emeritus
Try taking the limit of T as E approaches U0. Use the fact that 1-U0/E will approach 0 and approximate sin x by x when x ~ 0.

3. Jul 4, 2010

### graphene

You'll need to solve the Schrodinger equation with E = Uo.

Don't try to find T by putting E = Uo in those two cases. This is because the solution to $$\frac{{d}^{2}\psi}{d{x}^{2}} = k$$ is different for the three cases where k is positive, negative or zero. You cannot solve the equation for positive k, and then put k=0 in the solution to obtain the solution for k=0.
So you'll have to solve Schrodinger equation again with E = Uo inside the barrier.