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An iteration algorithm for the time-independent fractional Schrödinger equation with Coulomb potential

Marwan Al‐Raeei, Moustafa Sayem El‐Daher

PramanaOct 29, 202010 citations

The wave functions and energy levels of a Schrödinger equation with the potential being the sum of a harmonic oscillator potential, a linear potential, and a Coulomb potential

N. V. Maksimenko, S. M. Kuchin

Russian Physics JournalDec 1, 20102 citations

Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

Sepehr Hassanabadi, Jan Křı́ž, B. C. Lütfüoğlu +3 more

International Journal of Theoretical PhysicsDec 23, 20247 citations

On the exact discretization of Schrödinger equation

Chih‐Lung Chou

arXiv:2008.03698Physics Letters AOct 28, 20202 citations

Quantum mechanics and umbral calculus

J. E. López-Sendino, J. Negro, M. A. del Olmo +1 more

In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schrödinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schrödinger equation with a potential depending only in the space variable is discussed.In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schrödinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schrödinger equation with a potential depending only in the space variable is discussed.

Journal of Physics Conference SeriesAug 1, 20086 citations

Quantum mechanics and umbral calculus

E. Lopez-Sendino, J. Negro, M. A. del Olmo +1 more

In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schroedinger equation with a potential depending only in the space variable is discussed.In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schroedinger equation with a potential depending only in the space variable is discussed.

arXiv:0805.2017May 14, 20080 citations

Discrete coulomb potential

Abstract

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Discrete coulomb potential

Abstract

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