Consider the unbound states (E>0) of the finite square well . For a wave incident from the left, the solution to the Schrödinger equation can be written as .
a) Determine k and l.
b) Write down equations for all four boundary conditions for this problem.
c) Use the boundary conditions at x=+L to express C in terms of F and to express D in terms of F.
d) Use your results from c) and the boundary conditions at x=-L to eliminate A and to show that B can be expressed in terms of F as with .
e) Plot the transmission coefficient versus energy over a suitable range.
f) For which values of the energy is the transmission coefficient equal to 1?
Consider a particle with mass m and energy E>V0 incident from the left on a potential .
a) Write down the solution of Schrödinger’s equation for each region.
b) State the boundary conditions that apply and obtain a sufficient number of equations to determine all unknown constants.
c) Solve for the transmission coefficient and plot it versus energy over a suitable range.
d) For which values of the energy is the transmission coefficient equal to 1?
e) Which value does the transmission coefficient approach for E>>V0?