On physical analysis of numerical methods in the 1D Coulomb problem

Main Article Content

M. A. Carrillo-Bernal R. P. Martínez-y-Romero H. N. Núñez-Yépez A. L. Salas-Brito Didier A. Solís

Abstract

Diverse numerical studies of the 1D Coulomb problem have suggested the existence of an in nite binding-energy ground-state and de nite parity eigenstates in this system. We exhibit that such conclusions about the 1D Coulomb problem are wrong. The origin of the mistakes are to be found not in the numerical techniques employed but in the careless extrapolation of their results. Any numerical technique used for solving the 1D Coulomb problem must be supplemented by a detailed analysis of the e ect of the impenetrable barrier produced by the  jxj 1 singularity in order to obtain valid conclusions.

Article Details

How to Cite
CARRILLO-BERNAL, M. A. et al. On physical analysis of numerical methods in the 1D Coulomb problem. Quarterly Physics Review, [S.l.], v. 3, n. 3, oct. 2017. Available at: <http://journals.ke-i.org/index.php/qpr/article/view/1547>. Date accessed: 15 dec. 2017.
Section
Research Articles

References

V. S. Vrkljan, Zeits. Phys. 52, 735 (1928).
V. S. Vrkljan, Zeits. Phys. 54, 133 ( 1929).
R. Loudon, Am. J. Phys. 27, 649 (1959).
M. Andrews, Am. J. Phys. 34, 1194 (1966).
L. K. Haines, D. H. Roberts, Am. J. Phys. 37, 1145 (1969).
C. H. Mehta and S. H. Patil, Phys. Rev. A 17, 43 (1978).
F. Gesztezy, J. Phys. A: Math. Gen. 13 867 (1980).
C. Tzara, Phys. Lett. A 111, 343 (1985).
R. Kosloff, D. Kosloff, Journal of Computational Physics 63, 363 (1986).
H. N.N\'u\~nez-Y\'epez, C. A.Vargas, and A. L. Salas-Brito, Eur. J. Phys. 8, 189 (1987).
H.\ N.\ N\'u\~nez-Y\'epez and A.\ L.\ Salas-Brito, Eur.\ J. Phys.\ 8, 307 (1987).
H. N. N\'u\~nez-Y\'epez, C. A. Vargas, A. L. Salas-Brito, J. Phys. A: Math. Gen. 21, L651 (1988).
H. N. N\'u\~nez-Y\'epez, C. A. Vargas, A. L. Salas-Brito, J. Phys. A: Math. Gen. 21, L651 (1988).
R. Mart\'{\i}nez-y-Romero, C. A. Vargas, A. L. Salas-Brito, and H. N. N\'u\~nez-Y\'epez, Rev. Mex. Fis. 35, 617 (1989).
H. N. N\'u\~nez-Y\'epez, C. A. Vargas, and A. L. Salas-Brito, Phys. Rev. A 39, 4306 (1989).
H. N. N\'u\~nez-Y\'epez, C. A. Vargas, and A. L. Salas-Brito, Phys. Lett. A 142, 318 (1989).
T. Ogawa and T. Takagahara, Phys. Rev. B 43, 14325(R).
M. K. Kostov, M. W. Cole, and G. D. Mahan, Phys. Rev. B 66, 075407 (2002).
K. Burnett, V. C. Reed, and P. L. Knight, J. Phys. B 26, 561 (1993).\par
M. Moshinsky, J. Phys. A: Math. Gen. 26, 2445 (1993).
F. Sharifi, A. V. Herzog, and R. C. Dynes, Phys. Rev. Lett. 71, 428 (1993).
R. G. Newton, J. Phys. A: Math. Gen. 27, 4717 (1994).
W. Fischer, H. Leschke, P. M\"uller, J. Math. Phys. 36, 2313 (1995).
Yangqiang Ran, Lihui Xue, Sizhu Hu and Ru-Keng Su, J. Phys. A: Math. Gen. 33, 9265 (2000).
P. M. Platzman, M. I. Dykman, Science 284, 1967 (1999).
M. I. Dykman, P. M. Platzman, and P. Seddighrad, Phys. Rev. B 67, 155402 (2003);
M. Mineev, Theor. Math. Phys. 140, 1157 (2004).
G. S. Pogosyan, L. E. Vicent, and K. B. Wolf J. Math. Phys. 46, 072108 (2005).
X. Zhang and R. R. Jones, Phys. Rev. A 73, 035401 (2006).
G. Abramovici and Y. Avisai, J. Phys. A: Math. Theor. 42, 285302 (2009).
C. R. de Oliveira, Phys. Lett. A 374, 2805 (2010).
H. N. N\'u\~nez-Y\'epez, A. L. Salas-Brito, and Didier A. Solis, Phys. Rev. A 83, 064101 (2011).. N. N\'u\~nez-Y\'epez, A. L. Salas-Brito, and Didier A. Sol\'{\i}s, J. Phys. A: Math. Theor. 46, 208003 (2013).. J. Boya, M. Kmiecik, and A. Bohm, Phys. Rev. A, 37, 3567 (1988).. Dziubak and J. Matulewski, Optics Communications 290, 92 (2013).. H. Gebremedhin and C. A. Weatherford, Phys. Rev. E 89, 053319 (2014).. Schwengelbeck and F. H. M. Faisal, Phys. Rev. A 50, 632 (1994).
V. A. Harutyunyan, Physica E 57, 69 (2014).
W. Zhao, L. Wang, J. Bai, J. S. Francisco, and X. Cheng Zeng, J. Am. Chem. Soc. 136, 10661 (2014).
DOI: 10.1021/ja5041539. Hogreve, J. Phys. A: Math. Theor. 47, 125302 (2014).
H. N. N\'u\~nez-Y\'epez, A. L. Salas-Brito, and Didier A. Solis, Phys. Rev. A 89, 049908(E) (2014).
M. A. Carrillo-Bernal, H. N. N\'u\~nez-Y\'epez, A. L. Salas-Brito, and Didier A. Solis, Phys. Rev. E to appear (2015).
M. Moshinsky, N. M\'endez, E. Murow, J. W. Hughes, Ann. Phys. N. Y. 155, 231 (1984).. Mayle, B. Hezel, I. Lesanovsky, and P. Schmelcher, Phys. Rev. Lett. 99, 113004 (2007).. Xianxi, J. Dai, and J. Dai, Phys. Rev. A 55, 2617 (1997).
T. Giamarchi, Quantum Physics in One-Dimension (Oxford University Press, Oxford UK, 2014).
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++, 2nd. ed. (Cambridge University Press, New York, 2002).
\bibitem{kato} T. Kato, Perturbation theory for linear operators, (Springer-Verlag, Berlin, 1982).
E. Davies and M. Plum, IMA J. Numer. Anal. 24, 417 (2004).. Weidmann, Univ. Iagel. Acta Math. 34, 153 (1997).
M. M. Nieto, Phys. Rev. A 61, 034901 (2000).. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, (Dover, New York , 1965) p.\ 504.. Boulton, IMA J. Numer. Anal. 27, 102 (2007).
M. Lewin and \' E. S\'er\'e, Proc. London Math. Soc. 100, 864 (2010).
M. A. Robdera, A Concise Approach to Mathematical Analysis, (Springer-Verlag, Berlin, 2004).