Exact quantization formula for affine linearly energy-dependent potentials

Axel Schulze-Halberg 1
  • 1 Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN, 46408, USA

Abstract

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.

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  • [1] G. Arfken, Mathematical Methods for Physicists, (Academic Press, Orlando, 1985)

  • [2] F. Calogero, J. Math. Phys. 6, 161 (1965) http://dx.doi.org/10.1063/1.1704255

  • [3] K.M. Case, Phys. Rev. 80, 797 (1950) http://dx.doi.org/10.1103/PhysRev.80.797

  • [4] S.-H. Dong, A. Gonzalez-Cisneros, Ann. Phys. 323, 1136 (2008) http://dx.doi.org/10.1016/j.aop.2007.12.002

  • [5] M. De Sanctis, P. Quintero, Eur. Phys. J. A 39, 1434 (2009)

  • [6] G.F. Drukarev, JETP 19, 247 (1949)

  • [7] J. Formanek, R.J. Lombard, J. Mares, Czech. J. Phys. 54, 289 (2004) http://dx.doi.org/10.1023/B:CJOP.0000018127.95600.a3

  • [8] J. Garcia-Martinez, J. Garcia-Ravelo, J.J. Pena, A. Schulze-Halberg, Phys. Lett. A 373, 3619 (2009) http://dx.doi.org/10.1016/j.physleta.2009.08.012

  • [9] X.-Y. Gu, S.-H. Dong, Z.-Q. Ma, J. Phys. A. 42, 035303 (2009) http://dx.doi.org/10.1088/1751-8113/42/3/035303

  • [10] S.M. Ikhdair, R. Sever, J. Math. Chem. 45, 1137 (2009) http://dx.doi.org/10.1007/s10910-008-9438-8

  • [11] R.J. Lombard, J. Mares, Phys. Lett A 373, 426 (2009) http://dx.doi.org/10.1016/j.physleta.2008.12.009

  • [12] Z.-Q. Ma, B.-W. Xu, Europhys. Lett. 69, 685 (2005) http://dx.doi.org/10.1209/epl/i2004-10418-8

  • [13] A. Messiah, Quantum mechanics, (North-Holland, Amsterdam, 1961)

  • [14] W.E. Milne, Phys. Rev. 35, 863 (1930) http://dx.doi.org/10.1103/PhysRev.35.863

  • [15] L.I. Schiff, Quantum mechanics, (McGraw-Hill, New York, 1968)

  • [16] A. Schulze-Halberg, J. Garcia-Ravelo, J.J. Pena, Int. J. Mod. Phys. E 18, 1831 (2009) http://dx.doi.org/10.1142/S0218301309013890

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