, Volume 77, Issue 2, pp 243–261 | Cite as

Anharmonic solution of Schrödinger time-independent equation



We present here a mathematical explanation of how the Schrödinger equation for a class of harmonic oscillators possesses exact solutions. Some of the extended potentials used here are not present in the literature.


Anharmonic solutions; Yukawa potential. 


03.65.Ge; 33.10.Cs 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H Thomas, Structural phase transitions and soft modes edited by E J Samuelsen, E Andersen and J Feder (Universitetforlaget, Oslo, 1971), p-15.Google Scholar
  2. [2]
    V de Alfaro and T Regge , Potential scattering (North-Holland, Amsterdam, 1965)zbMATHGoogle Scholar
  3. [3]
    G P Flessas and K Das, Phys. Lett. A78, 19 (1980)MathSciNetADSGoogle Scholar
  4. [4]
    G P Flessas, J. Phys. A: Math. Gen. 14, L209 (1981)MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    G P Flessas, Phys. Lett. A81, 17 (1981)MathSciNetADSGoogle Scholar
  6. [6]
    P G L Leach, J. Math. Phys. 25, 2974 (1984)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. [7]
    A Khare, Phys. Lett. A83, 237 (1981)MathSciNetADSGoogle Scholar
  8. [8]
    E Magyari, Phys. Lett. A81, 116 (1981)MathSciNetADSGoogle Scholar
  9. [9]
    P M Morse and H Freshbach, Methods of theoretical physics (McGraw Hill Book Company, Inc., 1953) Vols I and IIGoogle Scholar
  10. [10]
    Z Yan, J. Phys. A: Math. Gen. 39, L401 (2006)Google Scholar
  11. [11]
    F Riesz and B Sz-Nagy, Functional analysis (Frederick Ungar Publishing Co., New York, 1978)Google Scholar
  12. [12]
    Z Rahman, Atmospheric and oceanic energetics and ocean-atmosphere geostrophic balance, Ph.D. Thesis (University of Chittagong, Nov. 1993)Google Scholar
  13. [13]
    Rajneesh Atre and Prasanta K Panigrahi, Phys. Lett. A317, 46 (2003)MathSciNetADSGoogle Scholar
  14. [14]
    R P Feynman, Nucl. Phys. B188, 479 (1981)MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    J N Islam, Proc. R. Soc. A389, 291 (1983)MathSciNetADSGoogle Scholar
  16. [16]
    J N Islam, Progr. Theor. Phys. 89, 161 (1993)MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    J N Islam, Found. Phys. (US) 24, 593 (1994)MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    J N Islam, Confinement and the Schrödinger equation for gauge theories, Book to appear in 2011.Google Scholar

Copyright information

© Indian Academy of Sciences 2011

Authors and Affiliations

    • 1
    • 2
    • 1
  1. 1.Research Centre for Mathematical and Physical SciencesUniversity of ChittagongChittagongBangladesh
  2. 2.Department of MathematicsUniversity of ChittagongChittagongBangladesh

Personalised recommendations