The Dunkl–Coulomb system in three-dimensions is introduced. The energy spectrum and the wave functions of the system are solved by means of spectrum generating algebra techniques based on the Lie algebra. An explicit h-spherical harmonics basis is given in terms of Jacobi polynomials.
The superintegrability of the Dunkl–Coulomb model in three-dimensions is studied. The symmetry operators generalizing the Runge–Lenz vector operator are given. Together with the Dunkl angular momentum operators and reflection operators they generate the symmetry algebra of the Dunkl–Coulomb Hamiltonian which is a deformation of
by reflections for bound states and is a deformation of
by reflections for positive energy states. The spectrum of the Hamiltonian is derived algebraically using this symmetry algebra. The analog of the functional relation between the Coulomb Hamiltonian, Runge–Lenz operator and the angular momentum is given.
In this work, the vibrational energy levels, the kinetic energy and the potential energy of the LiAr molecule in its X2Σ+ and A2Π electronic states are studied using the Morse potential and so(2, 1) spectrum generating algebra approach. An algorithm for the recursive evaluation of the expectation value of Zq = (e−α(r−re))q for a given state of Li(X2Σ+)Ar and Li(A2Π)Ar are proposed. As an application closed-form estimations for the value 〈r〉n of Li(X2Σ+)Ar and Li(A2Π)Ar were derived using Jensen’s inequality. This allows us to obtain several inequalities relating the radial expectation value 〈r〉n of Li(X2Σ+ )Ar and Li(A2Π)Ar at the logarithme of the expectation value of Zq = ( e−α(r−re) )q . These obtained outcomes are compared to the published results, both = theoretical and experimental, and show a good agreement.
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