Answer Happy

A beam of particles, each of the same mass and the same energy, travels in the positive x-direction. The beam is incident on an abrupt potential energy step at x = 0 and some of the beam is transmitted into the region x > 0 and the rest reflected. The energy eigenfunction describing the beam is v(x) = Aek + Be-k for a ≤ 0 Ceik2. for r > 0, where the coefficients A, B and C are constants and k₁ and k₂ are real constants. (a) Write down continuity boundary conditions at x = 0) to obtain two equations linking A, B and C. (b) Use the equations of part (a) to obtain an expression for the reflection coefficient. What fraction of the beam is reflected if k₁/k₂ = 2?