# Tunneling through step potential

1. Nov 25, 2008

### frankcastle

1. The problem statement, all variables and given/known data
Hey, I found this interesting case in the tunneling problem.
How do we calculate the transmission probability when the
energy of the approaching particle is equal to the height of the potential barrier?

I.e E=Vo.

2. Relevant equations

Same equations as in other cases for x<0.

3. The attempt at a solution
How does the particle behave in the potential step region?

2. Nov 25, 2008

### najima

can we calculate like the other problem of the potential barrier .E=V so after calculating Hamiltonian operator on wave function in part 1 we have Φ_1=Aexp(ikx)+Bexp(-ikx) and part 2 :Φ_2=0? and we can calculate A and B.

3. Nov 25, 2008

### frankcastle

The solution for part 1 makes sense, but why must the wave function be zero in the square potential region? If tunneling is possible for E<V then transmission must occur for E=V too I think

4. Nov 25, 2008

### najima

I got what was my mistake!! :-)
General solutions are Φ_1=Aexp(ikx)+Bexp(-ikx) and Φ_2=Cexp(iqx)+Dexp(-iqx)
as we know k^2=2mE(4pi^2)/h^2 and q=2mE(E-V)(4pi^2)/h^2
so Φ_2=C+D (transmission is constant)it makes sense,doesn't it?;-)