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


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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).


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