Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 24, 2010

Exact quantization formula for affine linearly energy-dependent potentials

  • Axel Schulze-Halberg EMAIL logo
From the journal Open Physics


We construct an exact quantization formula for Schrödinger equations with potentials thatdepend affine linearly on the energy, that is, they contain a term linear in the energy plus an energy-independent term. If such an energy-dependent potential admits a discrete spectrum and its ground state solution is known, our formula predicts the complete energy spectrum in exact form.

[1] G. Arfken, Mathematical Methods for Physicists, (Academic Press, Orlando, 1985) Search in Google Scholar

[2] F. Calogero, J. Math. Phys. 6, 161 (1965) in Google Scholar

[3] K.M. Case, Phys. Rev. 80, 797 (1950) in Google Scholar

[4] S.-H. Dong, A. Gonzalez-Cisneros, Ann. Phys. 323, 1136 (2008) in Google Scholar

[5] M. De Sanctis, P. Quintero, Eur. Phys. J. A 39, 1434 (2009) 10.1140/epja/i2008-10720-5Search in Google Scholar

[6] G.F. Drukarev, JETP 19, 247 (1949) 10.3109/17453674908991097Search in Google Scholar PubMed

[7] J. Formanek, R.J. Lombard, J. Mares, Czech. J. Phys. 54, 289 (2004) in Google Scholar

[8] J. Garcia-Martinez, J. Garcia-Ravelo, J.J. Pena, A. Schulze-Halberg, Phys. Lett. A 373, 3619 (2009) in Google Scholar

[9] X.-Y. Gu, S.-H. Dong, Z.-Q. Ma, J. Phys. A. 42, 035303 (2009) in Google Scholar

[10] S.M. Ikhdair, R. Sever, J. Math. Chem. 45, 1137 (2009) in Google Scholar

[11] R.J. Lombard, J. Mares, Phys. Lett A 373, 426 (2009) in Google Scholar

[12] Z.-Q. Ma, B.-W. Xu, Europhys. Lett. 69, 685 (2005) in Google Scholar

[13] A. Messiah, Quantum mechanics, (North-Holland, Amsterdam, 1961) Search in Google Scholar

[14] W.E. Milne, Phys. Rev. 35, 863 (1930) in Google Scholar

[15] L.I. Schiff, Quantum mechanics, (McGraw-Hill, New York, 1968) Search in Google Scholar

[16] A. Schulze-Halberg, J. Garcia-Ravelo, J.J. Pena, Int. J. Mod. Phys. E 18, 1831 (2009) in Google Scholar

Published Online: 2010-9-24
Published in Print: 2011-2-1

© 2010 Versita Warsaw

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

Downloaded on 23.2.2024 from
Scroll to top button