Standing waves in a funny Potential distribution

[frankcastle]

Homework Statement

The description of the potential distribution is given in the attached image.
The particle arrives from the left with E>V0.

write the solutions to the S.E in regions x<o and x between o and a

Homework Equations

I believe psi(x)= e^ikx+Re^-ikx in x<0
and psi(x)=Ae^iqx+Be^-iqx for x b/w o and a.

The Attempt at a Solution

My question is, since there is complete reflection occurring at x=a, can A=B in region x b/w 0 and a? If so, there will be destructive interference in the region, giving R=1, which is what we are asked to prove in the question. Is this approach of equating coefficients of wave traveling in +-x directions in this region applicable?

 

[turin]

The potential:
V=0 for x<0
V=V0 for 0<x<a
V->infinity for x>a

write the solutions to the S.E in regions x<o and x between o and a

I believe psi(x)= e^ikx+Re^-ikx in x<0
and psi(x)=Ae^iqx+Be^-iqx for x b/w o and a.

You have one boundary condition at x=a that relates A and B. You have two boundary conditions at x=0 that relate A, B and R. Once you have determined k and q (which I'm assuming you know how to do), then I believe you simply apply these boundary conditions.

 

[frankcastle]

thanks turin, I understand the problem well. My question is regarding the relation of the coefficients, A and B; with the respective intensities.

Since R=1 at x=a, I would immediately assume that B=A
instead of having to use Boundary conditions to find coefficients.
Would this be correct logic?

 

[turin]

Since R=1 at x=a, I would immediately assume that B=A
instead of having to use Boundary conditions to find coefficients.
Would this be correct logic?

No. You're contradicting yourself. You specified R for x<0, and now you want to talk about R at x=a, which doesn't even make sense, unless this is somehow a different R than the coefficient of the exponential that you originally gave. It's been a while since I solved one of these problems, so I can't remember if it should turn out that A=B is, in fact true; however, your logic to arrive at this conclusion is flawed.