Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 28, 2014

Schrödinger spectrum generated by the Cornell potential

Richard L. Hall and Nasser Saad
From the journal Open Physics

Abstract

The eigenvalues Ednl (a, c) of the d-dimensional Schrödinger equation with the Cornell potential V(r) = −a/r + c r, a, c > 0 are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is suffcient to know E(1, λ), and the envelope method provides analytic bounds for the equivalent complete set of coupling functions λ(E). Meanwhile the easily-implemented AIM procedure yields highly accurate numerical eigenvalues with little computational effort.

References

[1] J. Alford, M. Strickland, Phys. Rev. D 88, 105017 (2013)10.1103/PhysRevD.88.105017Search in Google Scholar

[2] H.-S. Chung, J. Lee, J. Korean Phys. Soc. 52, 1151 (2008)10.3938/jkps.52.1151Search in Google Scholar

[3] E. Eichten, K. Gottfried, T. Kinoshita, J. Kogut, K.D. Lane, T.- M. Yan, Phys. Rev. Lett. 34, 369 (1975) [Erratum-ibid. 36, 1276 (1976)].10.1103/PhysRevLett.36.1276Search in Google Scholar

[4] E. Eichten, K. Gottfried, T. Kinoshita, J. Kogut, K.D. Lane, T.-M. Yan, Phys. Rev. D 17, 3090 (1978)10.1103/PhysRevD.17.3090Search in Google Scholar

[5] E. Eichten, K. Gottfried, T. Kinoshita, J. Kogut, K.D. Lane, T.-M. Yan, Phys. Rev. D 21, 203 (1980)10.1103/PhysRevD.21.203Search in Google Scholar

[6] P.W.M. Evans, C.R. Allton, J.-I. Phys. Rev. D 89, 071502 (2014)10.1103/PhysRevD.89.071502Search in Google Scholar

[7] J.-K. Chen, Phys. Rev. D 88, 076006 (2013)10.1103/PhysRevD.88.034025Search in Google Scholar

[8] M. Hamzavi, A.A. Rajabi, Ann Phys.-New York 334, 316 (2013)10.1016/j.aop.2013.04.007Search in Google Scholar

[9] C.O. Dib, N.A. Neill, Phys. Rev. D 86, 094011 (2012)10.1103/PhysRevD.86.094011Search in Google Scholar

[10] G.S. Bali, Phys. Rep. 343, 1 (2001)10.1016/S0370-1573(00)00079-XSearch in Google Scholar

[11] D. Kang, E. Won, J. Comput. Phys. 20, 2970 (2008) 2970.Search in Google Scholar

[12] R.L. Hall, Phys. Rev. D 30, 433 (1984)10.1103/PhysRevD.30.433Search in Google Scholar

[13] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A: Math. Gen. 36, 11807 (2003)10.1088/0305-4470/36/47/008Search in Google Scholar

[14] R.L. Hall, Phys. Rev. D 22, 2062 (1980)10.1103/PhysRevD.22.2062Search in Google Scholar

[15] R.L. Hall, J. Math. Phys. 24, 324 (1983)10.1063/1.525683Search in Google Scholar

[16] R.L. Hall, J. Math. Phys. 25, 2078 (1984)10.1016/B978-0-12-556560-8.50007-3Search in Google Scholar

[17] R.L. Hall, Phys. Rev. A 39, 5500 (1989)10.1103/PhysRevA.39.5500Search in Google Scholar PubMed

[18] R.L. Hall, J. Math. Phys. 34, 2779 (1993)10.1063/1.530095Search in Google Scholar

[19] K. Atkinson, W. Han, Spherical harmonics and approximations on the unit sphere: An introduction (Springer, New York, 2012)10.1007/978-3-642-25983-8Search in Google Scholar

[20] D.J. Doren, D.R. Herschbach, J. Chem. Phys. 85, 4557 (1986)10.1063/1.451776Search in Google Scholar

[21] M. Reed, B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators, The appropriate discrete-spectrumresult for the linear-plus-Coulomb potential is given by Theorem XIII.69 (Academic Press, New York, 1978) 250Search in Google Scholar

[22] M. Abramowitz, I. Stegun, Handbook ofmathematical functions (Dover Publications, New York, 1965)Search in Google Scholar

[23] L.D. Landau, E.M. Lifshitz, QuantumMechanics: non-relativistic theory (Pergamon, London, 1981) Search in Google Scholar

Received: 2014-5-9
Accepted: 2014-8-12
Published Online: 2014-10-28
Published in Print: 2015-1-1

© 2015 Richard L. Hall, Nasser Saad

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow