Analytical Results on Generating Phase-Equivalent Potentials by Supersymmetry: Removal and Addition of Bound States

  • Géza Lévai
  • Daniel Baye
  • Jean-Marc Sparenberg
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 488)


Applying the techniques of supersymmetric quantum mechanics we determine closed algebraic expressions for potentials that are phase-equivalent with the generalized Pöschl—Teller potential. Among the examples we discuss the elimination of any single bound state, adding a single bound state at specific energies and eliminating the first few bound states. In our work we applied the abstract mathematical formalism developed recently for the modification of the spectrum of potentials without changing the phase shifts, and adapted it to the case of the generalized Pöschl—Teller potential. We discuss the importance of shape invariance in these procedures and comment on the possibility of deriving similar closed formulas for various other potentials.


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  1. Abramowitz M., Stegun I.A. (1970): Handbook of Mathematical Functions ( Dover, New York).Google Scholar
  2. Amado R.D. (1988): Phys. Rev. A 37, 2277ADSCrossRefGoogle Scholar
  3. Ancarani L.U., Baye D. (1992): Phys. Rev. A 46, 206ADSCrossRefMathSciNetGoogle Scholar
  4. Baye D. (1987): J. Phys. A 20, 5529ADSCrossRefMATHMathSciNetGoogle Scholar
  5. Baye D. (1993): Phys. Rev. A 48, 2040ADSCrossRefGoogle Scholar
  6. Baye D. (1994): in Quantum Inversion Theory and Applications, ed. von Geramb H.V., Lecture Notes in Physics 427 ( Springer, Berlin ) 127Google Scholar
  7. Baye D., Sparenberg J.-M. (1994): Phys. Rev. Lett. 73, 2789ADSCrossRefGoogle Scholar
  8. Baye D., Lévai G., Sparenberg J.-M. (1996): Nucl. Phys. A599, 435CrossRefGoogle Scholar
  9. Baye D., Sparenberg J.-M., Lévai G. (1996): contribution to this conference Ginocchio J.N. (1984): Ann. Phys. (N.Y.) 152, 203Google Scholar
  10. Gradshteyn I.S., Rhyzik I.M. (1965): Table of Integrals, Series and Products ( Academic, New York )Google Scholar
  11. Khare A., Sukhatme U. (1989): J. Phys. A 22, 2847ADSCrossRefGoogle Scholar
  12. Lévai G. (1994): in Quantum Inversion Theory and Applications, ed. von Geramb H.V., Lecture Notes in Physics 427 ( Springer, Berlin ) p. 107Google Scholar
  13. Sparenberg J.-M., Baye D. (1995): J. Phys. A 28, 5079ADSCrossRefMATHMathSciNetGoogle Scholar
  14. Sukumar C.V. (1985): J. Phys. A 18, 2917; 2937Google Scholar
  15. Swan P. (1963): Nucl. Phys. 46, 669CrossRefMathSciNetGoogle Scholar
  16. Talukdar B, Das U., Bhattacharyya C., Bera K. (1992): J. Phys. A 25, 4073ADSCrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Géza Lévai
    • 1
  • Daniel Baye
    • 2
  • Jean-Marc Sparenberg
    • 2
  1. 1.Institute of Nuclear ResearchHungarian Academy of SciencesDebrecenHungary
  2. 2.Physique Nucléaire Théorique et Physique Mathématique C.P. 229Université Libre de BruxellesBrusselsBelgium

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