An Alternative Method to Obtain Analytical Solutions of the Time-Independent Schrödinger Equation

Autor/inn/en	Morales, Juan C.; Arango, Carlos A.
Titel	An Alternative Method to Obtain Analytical Solutions of the Time-Independent Schrödinger Equation
Quelle	In: International Journal of Mathematical Education in Science and Technology, 54 (2023) 1, S.151-158 (8 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2022.2035003
Schlagwörter	Physics; Calculus; Mathematical Applications; Methods + Suchen Sie Ihr Suchwort? Physik; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Angewandte Mathematik; Innermathematische Anwendung; Method; Methode
Abstract	An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The differential equation resulting from operating the TISE on the product wave function is compared with a differential equation with a known solution. This comparison produces a system of differential equations for the integrating factor. This system of equations is easily solved for model quantum systems such as the harmonic oscillator, the hydrogen atom and the Morse oscillator. The method presented simplifies some approaches shown in textbooks, based on asymptotic analyses of the TISE, and power series methods with recurrence relations. In addition, the method presented here facilitates the understanding of the relationship between the ordinary differential equations of the mathematical physics and the TISE of physical models as the harmonic oscillator, the Hydrogen atom, and the Morse oscillator. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01