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

• Published in: Journal of mathematical chemistry 2009-04, Vol.45 (4), p.1137-1152
• Main Authors: Ikhdair, Sameer M., Sever, Ramazan
• Format: Article
• Language: English
• Subjects: Chemistry; Chemistry and Materials Science; Exact sciences and technology; Functional analysis; General and physical chemistry; Math. Applications in Chemistry; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Original Paper; Partial differential equations; Physical Chemistry; Sciences and techniques of general use; Theoretical and Computational Chemistry; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-008-9438-8

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, O 2 , N 2 and I 2 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 I 2 , LiH, HCl, O 2 , NO and CO are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.