Compute as a function of the incoming wave vector k, the quantum amplitudes (r(k), t(k), respectively) for scattering of left-incident particles from the potential of Figure 2.
Hints:
1. Your algebra will be simpler if you choose the solutions
of the form 
, 
, 
, and then
match the boundary conditions first at x=a and then at x=0.
Making similar guesses ``centering'' all parts of the wave function on
the right-most point in their interval, except for the right-most part
of the wave function
which should be centered on the left-most part of its interval, and
then solving the matching conditions in right to left order will make
the algebra in scattering problems. This approach is known as the
transfer matrix approach and is a general method for rending all
physical problems in one-dimension trivial in many advanced fields of physics.
2. You should find
for the transmission amplitude.