Lower Bounds on Transmission Probabilities in One-Dimensional Quantum Scattering Problems

Abstract

Quantum mechanics is the theory that describes dynamics of small objects such as atom and molecule. In this paper, Schrodinger’s wave mechanics, a part of quantum mechanics, is studied. The central equation of this wave mechanics is the Schrodinger’s equation. Solving this equation, quantum system dynamics can be described. In this work, the quantum scattering problem in one dimension is studied. Wave functions are obtained by exactly solving the Schrodinger’s equation in case of the delta function potential and the rectangular potential. The transmission and reflection probabilities are calculated from the obtained wave functions. Lower bounds on the transmission probabilities are presented. Finally, the lower bounds on the transmission probabilities are applied to the delta function potential and the rectangular potential problems. The results show that the exact transmission probabilities satisfy the lower bounds on the transmission probabilities.