Reflection and transmission probabilities from various potentials using quasilinearization and WKB approximation techniques

Kittinut Singhanat

Published Jan 1, 2025• 0 citations

Abstract

Quantum tunneling is a phenomenon in quantum mechanics. In this phenomenon, Quantum particle can go through potential barrier that potential energy is higher than total energy of quantum particle. Physicists are interested in transmitted and reflected value of Quantum particle that is transmission and reflection probabilities. Then, Schrödinger equation is used to find transmission and reflection probabilities by directly solving. However, some potential barriers are too complex to solve directly. Then, we use another method to solve more complex problem. That method is called "quasilinearization''. Quasilinearization method (QLM) is a numerical method to solve nonlinear differential equations. In this thesis, we compare the quasilinearization method with the well-known WKB approximation method. The results show that the transmission and reflection probabilities calculated by the QLM and WKB approximation have the same trend as the transmission and reflection probabilities calculated from the exact solution.

DOI: 10.58837/chula.the.2025.784

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