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Numerical Solution via Numerov Method of the 1D-Schrödinger Equation with Pseudo-Delta Barrier

Martinz S. D. G., Ramos R. V.

Computational Methods in Science and Technology

2018

Vol. 24, No. 3

177--185

In this work, aiming to solve numerically the Schrödinger equation with a Dirac delta function potential, we use the Numerov method to solve the time independent 1D-Schrödinger equation with potentials of the form V (x) + αβp(x), where δp(x) is a pseudo-delta function, a very high and thin barrier. The numerical results show good agreement with analytical results found in the literature. Furthermore, we show the numerical solutions of a system formed by three delta function potentials inside of an infinite quantum well and the harmonic potential with position dependent mass and a delta barrier in the center.