The Information-Theoretic Treatment of Spinless Particles with the Assorted Diatomic Molecular Potential

Abstract

The relativistic solutions of the Klein-Gordon equation comprising an interaction of the generalized inversely quadratic Yukawa potential mixed linearly with the hyperbolic Schiöberg molecular potential is achieved employing the idea of parametric Nikiforov-Uvarov and the Greene-Aldrich approximation scheme. The energy spectra and the corresponding normalized wave functions are derived regarding the hypergeometric function in a closed form for arbitrary ℓ -state. Numerical results of the energy eigenvalue are proposed. Moreover, special circumstances of this potential are reviewed, and their energy eigenvalues were assessed. Subsequently, the Tsallis entropy and Rényi entropy both in position and momentum spaces are defined under the desired potential. The impacts of these entropies on the angular momentum quantum number are explored in detail.

Thermal Responses and the Energy Spectral of Diatomic Molecules Using Nikiforov–Uvarov Methodology

“…Because of their diverse uses, solutions to the relativistic and non-relativistic wave equations have been used in various quantum potential interactions employing various methodologies [22,23]. These approaches include the 1/N shifted expansion procedure [24], the Nikiforov-Uvarov approach [25][26][27], the asymptotic iteration method [28], the factorization method [29,30], the formula technique [31], the supersymmetric approach [32,33], the ansatz methodology [34], the Laplace transform approach [35,36], the functional analysis approach [37,38], the appropriate quantization rule [39], and others [40,41]. For many solvable quantum frameworks, the hypergeometric Nikiforov-Uvarov technique has demonstrated its ability to determine the exact energy levels of bound states [42].…”

Effects of elliptic oblateness on harmonic oscillator in elliptic paraboloid potential

“…In particular, we can further analyze and discuss the problems related to the hydrogen atom through the relationship between the spatial harmonic oscillator and the hydrogen atom. In recent years, using the double wave function method, asymptotic iteration method, the Fourier transform method, and so on, some researchers study the problem of the onedimensional or isotropous quantum harmonic oscillator, in which significant results have been obtained [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In this paper, by the method of separating variables, the steady-state Schrodinger equation of a potential well of an infinite elliptic parabola is solved, and quantum properties of the harmonic oscillator in the potential well of an infinite elliptic parabola are analyzed and studied.…”