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Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

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  • Nasser Saad
  • Richard L. Hall
  • Hakan Çiftçi
  • Özlem Yeşiltaş

Abstract

We study the generalized quantum isotonic oscillator Hamiltonian given by ð » = − ð ‘‘ 2 / ð ‘‘ ð ‘Ÿ 2 + ð ‘™ ( ð ‘™ + 1 ) / ð ‘Ÿ 2 + 𠑤 2 ð ‘Ÿ 2 + 2 ð ‘” ( ð ‘Ÿ 2 − ð ‘Ž 2 ) / ( ð ‘Ÿ 2 + ð ‘Ž 2 ) 2 , ð ‘” > 0 . Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters ð ‘” , 𠑤 , and ð ‘Ž may be found to high accuracy.

Suggested Citation

  • Nasser Saad & Richard L. Hall & Hakan Çiftçi & Özlem Yeşiltaş, 2011. "Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential," Advances in Mathematical Physics, Hindawi, vol. 2011, pages 1-20, June.
    • Handle: RePEc:hin:jnlamp:750168
    DOI: 10.1155/2011/750168
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    Cited by:

    1. Yeşiltaş, Özlem, 2023. "The Black–Scholes equation in finance: Quantum mechanical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).

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