Consider particles incident (in one dimension) on a potential energy step with E>U.
(That is, particles of total energy E are directed along in one dimension from a region of U=0 to a region of E>U>0.)
Apply the boundary conditions for [tex]\Psi[/tex] and d[tex]\Psi[/tex]/dx to find the probabilities for the wave to be reflected and to be transmitted.
Evaluate the rations [|B'|^2]/[|A'|^2] and [|C'|^2]/[|A'|^2] and interpret these terms.
x<0: [tex]\Psi[/tex]1 = A'e^(ikx) + B'e^(-ikx)
x>0: [tex]\Psi[/tex]2 = C'e^(ik1x) + D'e^(-ik1x)
The Attempt at a Solution
I know that the boundary conditions are [tex]\Psi[/tex]1(x=0)=[tex]\Psi[/tex]2(x=0) and d[tex]\Psi[/tex]1(x=0)/dx.
But how do I find the probabilities for the wave to be reflected or transmitted? Would that happen to be those ratios? Because if |B'|^2 = |A|^2, then the whole wave is reflected, so the probability of it being reflected is 1.... AND the ratio would be 1.
So is that the right idea?