Paper Title :A Study Of The Finite Difference Methods And The WENO Schemes In The Resolution Of Schrodinger Equation

Author :Yacine Benhadid

Article Citation :Yacine Benhadid , (2016 ) " A Study Of The Finite Difference Methods And The WENO Schemes In The Resolution Of Schrodinger Equation " , International Journal of Mechanical and Production Engineering (IJMPE) , pp. 6-11, Volume-4,Issue-3

Abstract : The goal of this research was to examine the quantum mechanical phenomenon of tunneling with respect to the Schrödinger Equation. A quantum mechanical wave is said to “tunnel” when it travels (propagates) through a classically forbidden region. In a more physical interpretation, it is when the energy (E) of the wave is lower than the potential at a specific point V(x). [A point where V(x) is greater than E is referred to as a classical turning point.] The phenomenon of a tunneling was examined in a double-well potential. Another goal of this project was to compare two methods for approximating the tunneling time of a wave packet. The two methods used were the finite difference method and WENO approximation scheme In order to compare a potential that experienced tunneling and one that did not, the solution to a quadratic potential was also solved. Index Terms- WENO schemes, Finite difference, Schrodinger equation, Simulation.

Type : Research paper

Published : Volume-4,Issue-3

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