Applications of the numerical calculation for a resolution of transcendent equations in quantum mechanics

Abstract

Many students of physics and of certain courses of engineering are faced with the discipline of numerical calculation, developing it in a purely abstract way. In this way, this work aims at the use of numerical calculus as a tool to solve problems involving quantum mechanics in order to demonstrate in practice its application in obtaining and analyzing results in two specific problems: $\left(i\right)$ The double well symmetric potential $\delta \left(x\right)$. $\left(ii\right)$ And the square well infinite potential with a centered potential barrier, type $\delta \left(x\right)$. For these two cases we show that the possible solutions of allowed energies can be obtained by the numerical calculation, specifically by the method of the bisection. We also show that the parity of the wave function interferes directly in the allowed states and the effects on the particle subjected to these two potentials.

Keywords:
General Relativity; Field Theory; Gravitation; Abelian Votex