- #1
Aaron7
- 14
- 0
Homework Statement
There is a step barrier at x=0, V_0 > E
I am given:
ψi = e^i(kx−ωt) --->
ψr = R e^i(−kx−ωt) <---
ψt = T e^(−αx−iωt) --->
Part of question I am confused about: State the two boundary conditions satisfied by the wave function at x = 0 and hence find expressions for |R|^2 and |T|^2
Homework Equations
N/A
The Attempt at a Solution
I have already worked out an equation for alpha in the previous part.
ψ1 = ψi + ψr
ψ2 = ψt
I started to apply the conditions ψ1(0) = ψ2(0) to get 1 + R = T
and d/dx ψ1(0) = d/dx ψ2(0) to get ik - iRk = -αT
I solved the above to get R = (ik +αT) / ik with T = 1 + R etc
I understand that |R|^2 = R x R* and |T|^2 = T x T*
However I am told that T = 1 - R since these are probability coefficients. Do I solve with T = 1-R (probability coefficients) or T = 1+R (using ψ1(0) = ψ2(0))? I am confused which one to use and why.
Many thanks.