Exactly Solvable Models for the Generalized Schrödinger Equation

Suzko, A. A.; Velicheva, E. P.

doi:10.1007/978-3-642-28212-6_18

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2023

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“…In that circumstances, it is necessary to study how to make corrections to these models or even to examine the obtaining of approximate solutions. In the framework of nonrelativistic quantum mechanics, the Schrödinger equation describes precisely the dynamics of a closed quantum system, providing all the information about the properties of the system [1]. In this context, several examples of exactly solvable models, like the harmonic oscillator [2], the two-body problem with non-central forces [3], the modified ring-shaped oscillator potential [4], and a model involving a class of hyperbolic potential well [5].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solutions of the Schrödinger Equation with Hulthén Potential in the Global Monopole Spacetime

et al. 2023

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In this paper, we studied the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also considered that the electron is influenced by the Hulthén potential. In particular, we dealt with the Schrödinger equation in the presence of a global monopole. We obtained approximate solutions for the problem, determined the scattering phase shift and the S-matrix, and analyzed bound states.

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