Quantum Spectrum of Some Anharmonic Central Potentials: Wave Functions Ansatz

Abstract

Based on the ansatz to the wave functions, the quasi-exact solutions of the 2D Schrödinger equation with some anharmonic potentials are reviewed and analyzed if admitting restrictions on the parameters of the potential and the angular momentum m. These potentials are taken as the screened Coulomb potential V(r)=a/r+b/(r+λ), the singular one-fraction power one V(r)=ar −1/2+br −3/2 and the singular two-fraction one V(r)=ar 2/3+br −2/3+cr −4/3. The latter one is found that the hidden symmetry exists if substituting r→−ir. It will reverse the signs of E and c of quantum system, leaving the remaining parameters invariant.

This is a preview of subscription content, access via your institution.

REFERENCES

  1. 1.

    S. K. Bose and N. Gupta, Nuovo Cimento B 113, 299 (1998).

    ADS  MathSciNet  Google Scholar 

  2. 2.

    M. S. Child, S. H. Dong, and X. G. Wang, J. Phys. A: Math. Gen. 33(32), 5653 (2000).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    S. H. Dong, Inter. J. Theor. Phys. 39(4), 1119 (2000); 40(2), 559 (2001); Physica Scripta 65(4), 289 (2002).

    Article  Google Scholar 

  4. 4.

    S. H. Dong and Z. Q. Ma, J. Phys. A: Math. Gen. 31, 9855 (1998).

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    S. H. Dong, Z. Q. Ma, and G. Esposito, Found. Phys. Lett. 12, 465 (1999).

    MathSciNet  Article  Google Scholar 

  6. 6.

    S. K. Bose, Hadronic J. 16No 2, 99 (1993).

    MathSciNet  Google Scholar 

  7. 7.

    A. Schulze-Halberg, Hadronic J. 24No. 5, 519 (2001).

    MathSciNet  Google Scholar 

  8. 8.

    G. Esposito, J. Phys. A: Math. Gen. 31, 9493 (1998); Found. Phys. Lett. 11, 535 (1998); 13(1), 29 (1998).

    ADS  MathSciNet  Article  Google Scholar 

  9. 9.

    B. Gonul, O. Ozer, M. Kocak, D. Tutcu, and Y. Cancelik, J. Phys. A: Math. Gen. 34(40), 8271 (2001).

    ADS  MathSciNet  Article  Google Scholar 

  10. 10.

    R. S. Kaushal, Ann. Phys. 206, 90 (1991).

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    A. Schulze-Halberg, Found. Phys. Lett. 13(3), 265 (2000).

    MathSciNet  Article  Google Scholar 

  12. 12.

    M. Znojil, J. Math. Phys. 31, 108 (1990).

    ADS  MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dong, SH., San, GH. Quantum Spectrum of Some Anharmonic Central Potentials: Wave Functions Ansatz. Found Phys Lett 16, 357–367 (2003). https://doi.org/10.1023/A:1025313809478

Download citation

  • anharmonic potential
  • quantum spectrum
  • wave functions
  • ansatz
  • hidden symmetry