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On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom

DOI: 10.4236/cn.2010.21009, PP. 62-64

Keywords: one-dimensional hydrogen atom, one-dimensional Coulomb potential, supersymmetric quantum mechanics.

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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.

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.

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