Método WKB como alternativa para solução de problemas no formalismo do PDTO

Abstract

The main objective of the present work is to show that the Wentzel, Kramers, Brillouin(WKB) method can be used together with the Position dependent translation operator (PDTO) formalism to obtain the correct energies for the cases of the potential of an infinite square well and the harmonic potential. For this, it was necessary to briefly introduce the usual formalism of quantum mechanics and the WKB method in this same formalism. Then, we made an introduction to the PDTO formalism and the WKB method modified for this formalism. Finally, we apply everything discussed for the cases of the potential of an infinite square well and the harmonic potential, both in a deformed space, thus obtaining the expected energies, showing that the WKB method is a viable alternative to obtain the solutions of a Schrödinger-like equation in the PDTO formalism, which can be applied to other problems in future works.