On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom
R. P. Martínez-y-Romero, H. N. Núnez-Yépez, A. L. Salas-Brito
.
DOI: 10.4236/cn.2010.21009   PDF   HTML     4,865 Downloads   9,127 Views   Citations

Abstract

The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al. [1] In doing so they address the peculiar system known as the one-dimensional hydrogen atom. In this paper we show that their remarks on such problem are mistaken. We do this by explicitly constructing both the one-dimensional Coulomb potential and the superpotential associated with the problem, objects whose existence are denied in the mentioned paper.

Share and Cite:

R. Martínez-y-Romero, H. Núnez-Yépez and A. Salas-Brito, "On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom," Communications and Network, Vol. 2 No. 1, 2010, pp. 62-64. doi: 10.4236/cn.2010.21009.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. Morales, J. J. Pe?a, J. L. López-Bonilla, and J. Mol. Struct. (Teochem), Vol. 621, pp. 19, 2003.
[2] M. J. Lighthill, “Fourier analysis and generalized functions, cambridge university press,” Cambridge, 1975.
[3] R. P. Martínez-Romero, C. A. Vargas, A. L. Salas-Brito, and H. N. Núnez-Yépez, Rev. Mex. Fis., Vol. 35, pp. 617, 1989.
[4] B. Jaramillo, R. P. Martínez-y-Romero, H. N. Núnez- Yépez,and A. L. Salas-Brito, Phys. Lett. A, Vol. 374, pp. 150, 2009.
[5] H. N. Núnez-Yépez, C. A. Vargas, A. L. Salas-Brito, Eur. J. Phys., Vol. 8, pp. 189, 1987.
[6] H. N. Núnez-Yépez, C. A. Vargas, A. L. Salas-Brito, J. Phys. A, Math. Gen., Vol. 21, pp. L651, 1988.
[7] I. Tsutsui, T. Fülop, and T. Cheon, J. Phys. A: Math. Gen. Vol. 36, pp. 275, 2003.
[8] T. D. Imbo and U. P. Sukhatme, Phys. Rev. Lett., Vol. 54, pp. 2184, 1985.
[9] H. N. Núnez-Yépez, C. A. Vargas, A. L. Salas-Brito, Phys. Rev. A, Vol. 39, pp. 4307, 1989.
[10] P. Pfeifer, “Dissertation, Eidgenossiche Technisch Hoch- schule,” Zürich, 1980.
[11] P. Pfeifer, in J. Hinze ed. Energy Storage and Redistribution in Molecules, Plenum Press, New York, pp. 315, 1983.
[12] R. P. Martínez-Romero, H. N. Núnez-Yépez, A. L. Salas-Brito, “A simple introduction to superselection rules in nonrelativistic quantum mechanics can be found in C. Cisneros,” Eur. J. Phys. Vol. 19, pp. 237, 1998.
[13] L. J. Boya, M. Kmiecik, A. Bohm, Phys. Rev. A., Vol. 37, pp. 3567, 1988.
[14] R. G. Newton, J. Phys. A: Math. Gen., Vol. 27, pp. 4717, 1994.
[15] U. Oseguera, M. de Llano, and J. Math. Phys. Vol. 43, pp. 4575, 1993.
[16] W. Fischer, H. Leschke, P. Muller, and J. Math. Phys., Vol. 36, pp. 2313, 1995.
[17] M. M. Nieto, Phys. Rev. A, Vol. 61, pp. 034901, 2000.
[18] C. R. de Oliveira and A. A. Verria, Annals of Physics Vol. 324, pp. 251, 2009.
[19] S. Nouri, Phys. Rev. A, Vol. 65, pp. 062108, 2002.
[20] R. P. Martínez-Romero, H. N. Nú?ez-Yépez, A. L. Salas-Brito, and C. A. Vargas, “Actas de la 3a. Reunión Latinoamericana de Colisiones Atómicas, Moleculares y Electrónicas,” CNEA, Bariloche, Argentina, 1989.
[21] W. Rossner, G. Wunner, H. Herold, and H. Ruder, J. Phys. B: At. Mol. Opt. Phys., Vol. 17, pp. 29, 1984.
[22] W. Edelstein and H. N. Spector, Phys. Rev. B, Vol. 39, pp. 7697, 1989.
[23] M. W. Cole and M. H. Cohen, Phys. Rev. Lett. Vol. 23 pp. 1238, 1969. M. W. Cole, Phys. Rev. B, Vol. 2, pp. 4239. 1970.
[24] H. Ruder, G. Wunner, H. Herold, and F. Geyer, “Atoms in strong magnetic fields,” Springer Verlag, Berlin, 1994.
[25] S. H. Patil, Phys. Rev. A, Vol. 64, pp. 064902, 2001.
[26] G. Abramovici and Y. Avishai, J. Phys. A: Math. Theory, Vol. 42, pp. 28532, 2009.
[27] F. Cooper and J. G. Ginocchio, A. Khare, Phys. Rev. D, Vol. 36, pp. 2458, 1987.
[28] R. Montemayor and L. D. Salem, Phys. Rev. A, Vol. 40, pp. 2170, 1989.
[29] R. P. Martínez-Romero and H. N. Nú?ez-Yépez, A. L. Salas-Brito, Phys. Lett. A, Vol. 142, pp. 318, 1989.
[30] J. Benítez, R. P. Martínez-y-Romero, H. N. Núnez-Yépez, and A. L. Salas-Brito, Phys. Rev. Lett. Vol. 64, pp. 1643. 1990.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.