R-separable solutions of the Schrödinger equation

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.23.020203

Keywords:

Schr¨odinger equation, separability, propagator

Abstract

We present two examples where the Schrödinger equation admits R-separable solutions. In one of them (a particle in a uniform force field) the Schrödinger equation admits separable and R-separable solutions.

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References

N.N. Lebedev, Special Functions and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1965) (Dover, New York, reprinted 1972). Sec. 8.10

P. Moon and D.E. Spencer, Field Theory Handbook, Including Coordinate Systems, Differential Equations and Their Solutions, 2nd ed. (Springer-Verlag, Berlin, 1988). Sec. IV. https://doi.org/10.1007/978-3-642-83243-7

G.F. Torres del Castillo, An Introduction to Hamiltonian Mechanics (Springer, Cham, 2018), Sec. 6.1.3. https://doi.org/10.1007/978-3-319-95225-3

L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory), 3rd ed. (Pergamon, Oxford, 1991). §24

H.J.W. Müller-Kirsten, Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral, 2nd ed. (World Scientific, Singapore, 2012). Sec. 13.3. https://doi.org/10.1142/8428

G.F. Torres del Castillo and C. Sosa Sánchez, Solutions of the Schrödinger equation given by solutions of the Hamilton-Jacobi equation, Rev. Mex. Fís. 62 (2016) 534. https://doi.org/10.31349/RevMexFis.62.6.534

G.F. Torres del Castillo, op. cit., Example 6.15

F. Soto-Eguibar and H.M. Moya-Cessa, Solution of the Schrödinger Equation for a Linear Potential using the Extended Baker–Campbell–Hausdorff Formula, Appl. Math. Inf. Sci. 9 (2015) 175. https://dx.doi.org/10.12785/amis/090123

D.C. Khandekar and S.V. Lawande, Feynman path integrals: Some exact results and applications, Phys. Rep. 137 (1986) 115. https://doi.org/10.1016/0370-1573(86)90029-3

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Published

2026-07-01

How to Cite

[1]
G. F. Torres del Castillo, “R-separable solutions of the Schrödinger equation”, Rev. Mex. Fis. E, vol. 23, no. 2, pp. 1–4, Jul. 2026.

Issue

Vol. 23 No. 2 (2026): Revista Mexicana de Física E

Section

Education in Physics

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Copyright (c) 2026 Gerardo Francisco Torres del Castillo

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