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Mikulski D.,Gen. Zamoyska and Helena Modrzejewska High School | Eder K.,Gen. Zamoyska and Helena Modrzejewska High School | Konarski J.,Adam Mickiewicz University
Journal of Mathematical Chemistry | Year: 2014

For a high accuracy description of bond-stretching vibrations of diatomic molecules new analytic five and six-parameter potential energy functions have been proposed. These potentials include parameters that can be determined with the use of a direct fit to measured energy level spacings. The corresponding stationary radial Schrödinger equations with these potential energy functions are solved analytically, in an approximate scheme for zero total angular momentum. It is found that the wave functions for bound states can be expressed in terms of the Jacoby polynomial. The analytical expressions for purely vibrational energy levels have been derived within the algebraic approach. The potentials presented can be very useful for theoretical spectroscopic studies to reproduce the vibrational spectra of diatomic molecules. © 2014 The Author(s). Source


Mikulski D.,Gen. Zamoyska and Helena Modrzejewska High School | Eder K.,Gen. Zamoyska and Helena Modrzejewska High School | Konarski J.,Adam Mickiewicz University
Journal of Mathematical Chemistry | Year: 2014

A new approach for perturbation method, based on the Fredholm integral equation of the second kind has been introduced to theoretical physics and quantum chemistry. The method has been used in order to derive an analytical form of the υ-vibrational wavefunction in a form of a continuously convergent Liouville– Neumann perturbation series and to generate consecutive perturbation corrections to the wavefunction. The second-order correction to the energy levels has been obtained. Iterated kernels and a resolvent have been constructed and employed to the calculation of the wavefunction perturbation corrections. The method proposed can be used successfully in advanced calculations of quantum chemistry and theoretical spectroscopy because of a continuously convergence of the perturbation series. © The Author(s) 2014. Source


Mikulski D.,Gen. Zamoyska and Helena Modrzejewska High School | Konarski J.,Adam Mickiewicz University | Eder K.,Gen. Zamoyska and Helena Modrzejewska High School | Molski M.,Adam Mickiewicz University | Kabacinski S.,Poznan University of Technology
Journal of Mathematical Chemistry | Year: 2015

The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules. © 2015, Springer International Publishing Switzerland. Source

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