Phase Regularization and Additional Potential in Quantum Systems at the Potential Barrier to Maintain Adiabatic Condition

Abstract

This research is theoretical research with a literature study that examines methods to maintain characteristics of electrons when moving in a quantum system at the potential barrier. Attempts to maintain the characteristics of electrons in quantum systems are known as adiabatic. The method used in this research is the fast-forward method. This method was first introduced by Masuda and Nakamura in 2010. The fast-forward method is applied to barrier potential in case of electron energy larger and smaller than the potential barrier. This research focuses on preserving the characteristics of electrons by determining the regularization phase and additional potential of the quantum system at the barrier potential. The wave function solution of the system at the potential barrier is approximated by the Schrödinger equation into three regions for each case. The wave function of each region is regularized to be an adiabatic wave function and an additional term in the form of regularization phase (θ) is obtained. Given the regularized Hamiltonian, the additional potential (Ṽ) is obtained. The obtained regularization phase and additional potential ensure the quantum system at the potential barrier is in the same state from the initial state to the final state