The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech^2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz Landau L D and Lifshitz E M 1977 Quantum Mechanics (Non-relativistic Theory) (New York: Pergamon), which proves that ATMM is a simple and effective method for quantum reflection.