Abstract

FERNANDEZ-ROJAS, Carlos J.  and  FERNANDEZ-ROJAS, Freddy. An series solution for square-well potential. Novasinergia [online]. 2021, vol.4, n.2, pp.38-47.  Epub Dec 01, 2021. ISSN 2631-2654.  https://doi.org/10.37135/ns.01.08.02.

Abstract: In this work we study the problem of a particle in a finite square potential well. The eigenvalues corresponding to the Hamiltonian of the previous problem are found by a method which combines the Lagrange inversion theorem with a relation of recurrence to calculate derivatives of higher order of an inverse function. The methodology used allowed us to obtain a solution in of power for the finite square well potential that depend on the principal quantum number and of the force of attraction. On the other hand, our results reproduce, as special cases, general expressions of the eigenvalues for a particle located at the bottom of the well, in the middle of the well and at the top of the potential well. The calculated energies are compared with the exact solutions of the transcendental equation for the finite well.

Keywords : Energy levels; inversion methods; Schrödinger equation; potential well; series solution.

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