New method to solve certain differential equations

Rajchel, Kazimierz; Szczęsny, Jerzy

doi:10.1515/aupcsm-2016-0009

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New method to solve certain differential equations

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 15 (2016): Issue 1 (December 2016)

By: Kazimierz Rajchel and Jerzy Szczęsny

Open Access

|Dec 2016

Abstract

A new method to solve stationary one-dimensional Schroedinger equation is investigated. Solutions are described by means of representation of circles with multiple winding number. The results are demonstrated using the well-known analytical solutions of the Schroedinger equation.

References

[1] Dubrovin, Boris A., and Anatoliĭ T. Fomenko, and Sergeĭ P. Novikov. Modern geometry-methods and applications. Part II. The geometry and topology of manifolds. New York: Springer-Verlag, 1985. Cited on 107.
Search in Google Scholar Back to article
[2] Shankar, Ramamurti. Principles of quantum mechanics. 2nd ed. New York: Plenum Press, 1994. Cited on 108.
Search in Google Scholar Back to article
[3] Junker, Georg. Supersymmetric methods in quantum and statistical physics. Berlin: Springer-Verlag, 1996. Cited on 108.
Search in Google Scholar Back to article
[4] Walter, Wolfgang. Ordinary differential equations. New York: Springer-Verlag, 1998. Cited on 109.
Search in Google Scholar Back to article
[5] Cooper, Fred, and Avinash Khare, and Uday Sukhatme. “Supersymmetry in Quantum Mechanics.” Phys. Rep. 251, no. 5-6 (1995): 267–385. Cited on 109.
Search in Google Scholar Back to article
[6] Reid, William T. “Ricatti Differential Equations.” New York, London: Academic Press, 1972. Cited on 109.
Search in Google Scholar Back to article
[7] Rajchel, Kazimierz. “New solvable potentials with bound state spectrum.” Acta Physica Polonica B. (submitted). Cited on 110.
Search in Google Scholar Back to article

DOI: https://doi.org/10.1515/aupcsm-2016-0009 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 107 - 111

Submitted on: Oct 20, 2016

Accepted on: Nov 12, 2016

Published on: Dec 23, 2016

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

differential equation,

Schroedinger equation,

unit circle

Related subjects:

Mathematics,

General mathematics

© 2016 Kazimierz Rajchel, Jerzy Szczęsny, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

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