New method to solve certain differential equations

Karzimierz Rajchel, Jerzy Szczęsny

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.

Keywords


differential equation; Schroedinger equation; unit circle

Mathematics Subject Classification (2010)


35A24; 81Q99

References


Dubrovin, Boris A., and Anatolii T. Fomenko, and Sergei P. Novikov. Modern geometry-methods and applications. Part II. The geometry and topology of manifolds. New York: Springer-Verlag, 1985.

Shankar, Ramamurti. Principles of quantum mechanics. 2nd ed. New York: Plenum Press, 1994.

Junker, Georg. Supersymmetric methods in quantum and statistical physics. Berlin: Springer-Verlag, 1996.

Walter, Wolfgang. Ordinary differential equations. New York: Springer-Verlag, 1998.

Cooper, Fred, and Avinash Khare, and Uday Sukhatme. "Supersymmetry in Quantum Mechanics." Phys. Rep. 251, no. 5-6 (1995): 267-385.

Reid, William T. "Ricatti Differential Equations" New York, London: Academic Press, 1972.

Rajchel, Kazimierz. "New solvable potentials with bound state spectrum." Acta Physica Polonica B. (submitted).


Full Text: PDF

Download statistics: 1418

Licencja Creative Commons
This article by Karzimierz Rajchel, Jerzy Szczęsny is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej