Quantum Mechanical Transmission with Absorption

Transmission and reflection across a rectangular barrier at energies below and above barrier is the most commonly studied topic in non-relativistic quantum mechanics. However the subtle inter-relationship between the barrier problem and the corresponding well problem is not widely known, in particular when absorption is present. In this article we show that when a particle traverses an absorptive medium, at any given energy the absorption peaks for a particular value of absorption potential strength W0. Similarly we study the corresponding cases when incident energy E is increased keeping W0 constant. Further, we show that for a given E when W0. is made very large absorption gradually decreases and reflection overtakes it and tends towards unity. We also study the case of transmission across a potential barrier and well and interpret physically the behavior of absorption, transmission and reflection