1. The problem statement, all variables and given/known data We have a double step potential described by -V0 for |x| < a/2 0 otherwise. That is, three regions separated at -a/2 and a/2 with 0, -V0 and 0 We have a particle coming from the left with E > 0. Find the transmission amplitude S(E) 2. Relevant equations 3. The attempt at a solution To begin with I have "moved" everything by a/2 so the first step is at 0 and the second at a, to simplify things. Now I see two possible ways to do it. The first one is to 1) Find a solution for each of the three regions, which will involve defining 6 constants. 2) Setting the constant that corresponds to a particle coming from the right to 0, reducing it to 5 constants . 3) Use the normalization and continuity conditions on the wavefunction and its derivative at 0 and a will yield 5 equations, with which in principle I can solve for the constants. 4) Identify the solution corresponding to the particle being in the third region (transmitted) and find the transmission probability. The second one is 1) Treat it as two scattering processes for a particle of energy E, one with a step from 0 to -V0 at x=0 and other with a step from -V0 to 0 at x=a. 2) Find the transmission probabilities of both processes. 3) The total trnasmission probability is the product of both probabilities. Now, questions about this: a) The transmission probability is the integral over ALL space of the wavefunction for the third region. Is that right? b) Is the transmission "amplitude" just the (positive) root square ot the transmission probability? c) Is the second method even possible or do I have to consider the infinite reflections and transmissions that the first transmitted wave will suffer inside the well? I guess is the latter, since later on I'm asked to find something called the ressonance factor. d) In the case I have to consider the reflections between the steps can you give me a hint on where to start? Does my first method already account for this or do I have to postulate an infinite linear combination of solutions in the second region? e) In the second method (assuming it is right) can I change the values of the second step so that it is at x=0 and from 0 to +V0? And finally, can you recommend me any book where this problem is treated? Thank you for four time.