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The supersymmetric quantum mechanics theory and Darboux transformation for the Morse oscillator with an approximate rotational term

Abstract

Anharmonic potentials with a rotational terms are widely used in quantum chemistry of diatomic systems, since they include the influence of centrifugal force on motions of atomic nuclei. For the first time the Taylor-expanded renormalized Morse oscillator is studied within the framework of supersymmetric quantum mechanics theory. The mathematical formalism of supersymmetric quantum mechanics and the Darboux transformation are used to determine the bound states for the Morse anharmonic oscillator with an approximate rotational term. The factorization method has been applied in order to obtain analytical forms of creation and annihilation operators as well as Witten superpotential and isospectral potentials. Moreover, the radial Schrödinger equation with the Darboux potential has been converted into an exactly solvable form of second-order Sturm–Liouville differential equation. To this aim the Darboux transformation has been used. The efficient algebraic approach proposed can be used to solve the Schrödinger equation for other anharmonic exponential potentials with rotational terms.

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Correspondence to Damian Mikulski.

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Mikulski, D., Eder, K. & Konarski, J. The supersymmetric quantum mechanics theory and Darboux transformation for the Morse oscillator with an approximate rotational term. J Math Chem 52, 1552–1562 (2014). https://doi.org/10.1007/s10910-014-0335-z

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  • DOI: https://doi.org/10.1007/s10910-014-0335-z

Keywords

  • Factorization method
  • rotating Morse oscillator
  • Supersymmetric quantum mechanics
  • Darboux transformation
  • Pekeris transformation
  • Superpotential