All Title Author
Keywords Abstract

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.

Full-Text   Cite this paper   Add to My Lib


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.


[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.


comments powered by Disqus