Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng–Fan Potential

Abstract

By applying continuity and boundary conditions, the reflection and transmission coefficients of one-dimensional time-independent Schrödinger equation with a symmetric IntroductionThe scattering phenomena, such as scattering phase shifts, reflection and transmission coefficients are used to explain the behaviour of waves incident on a barrier [1-2]. The transmission coefficient represents the probability flux of the transmitted wave relative to that of the incident wave. It is often used to describe the probability of a particle tunneling through a barrier. This is more feasible in the case where electrons tunnel between two conducting materials. The shifted Deng-Fan potential is a suitable model for the theoretical predictions because it has been used extensively in both relativistic and non -relativistic quantum mechanics. The original Deng-Fan molecular potential has the correct asymptotic behaviour at the origin [3][4][5][6][7][8][9], and so, it has been used to predict the interactions between atoms and molecules and vibrational spectrum [3][4][5][6][7][8][9].

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

“…Consequent upon these, the exact and approximate solutions to the Schrödinger equation with diverse potential models have been obtained in no small measure using different types of approximations and methods (see Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and other references therein).…”