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Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules

Abstract

For arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D ≥ 2) hyperradial Schrödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact bound state energy eigenvalues (E nl ) are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (ψ nl (r)) are also calculated. The exact energy eigenvalues for these Kratzer-type potentials are calculated numerically for a few typical LiH, CH, HCl, CO, NO, O2, N2 and I2 diatomic molecules for various values of n and l quantum numbers. Numerical tests using the energy calculations for the inter dimensional degeneracy (D = 2 − 4) for I2, LiH, HCl, O2, NO and CO are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.

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Correspondence to Ramazan Sever.

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Ikhdair, S.M., Sever, R. Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules. J Math Chem 45, 1137–1152 (2009). https://doi.org/10.1007/s10910-008-9438-8

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  • DOI: https://doi.org/10.1007/s10910-008-9438-8

Keywords

  • Bound states
  • Modified Kratzer potential
  • Exact quantization rule
  • Diatomic molecules