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Physica Scripta

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

Y B Ateş, Eser Olğar

Published Apr 24, 2024• 1 citation
Publisher

Abstract

Abstract The effect of isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Kratzer, Mie and Hulthen potentials is obtained for any quantum states in the presence of constant form factor ε r = γ ρ 0 . The corresponding energy eigenvalues and eigenfunctions are determined and tabulated for a set of finite quantum numbers n and l in the framework of the well-known Nikiforov-Uvarov method.

DOI
10.1088/1402-4896/ad42da

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Abstract The effect of isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Kratzer, Mie and Hulthen potentials is obtained for any quantum states in the presence of constant form factor ε r = γ ρ 0 . The corresponding energy eigenvalues and eigenfunctions are determined and tabulated for a set of finite quantum numbers n and l in the framework of the well-known Nikiforov-Uvarov method.
Abstract The energy spectrum of the velocity-dependent potentials with respect to the harmonic oscillator potential and Coulomb potential are obtained for any n and l quantum states using the Nikiforov–Uvarov method for different cases of velocity-dependent terms. The effects of isotropic velocity-dependent potentials on the bound state energy eigenvalues are examined in analytic form when the form factor is considered as ξ ( r ) = γ r and ξ ( r ) = γ r 2 . As an application to a physical system, we evaluated the vibrational partition function and other thermodynamic properties for the isotropic velocity-dependent potential harmonic oscillator.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.