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Öğe An extension of quantum Hamilton-Jacobi formalism to N-spatial dimensions and its applications(Springer Heidelberg, 2023) Durmus, Aysen; Ozfidan, AyselDue to the importance of hyperspherical coordinates, we report the quantum Hamilton-Jacobi formalism in N=2 spatial dimensions. The quantum momentum function equations in N-dimensions have been constructed within the framework of non relativistic theory. We also study the singularity structure of the quantum momentum function, which yields the determination of the bound state spectra of stationary quantum systems. In order to confirm the reliability of quantum Hamilton-Jacobi formalism in N-dimensions, we present the numerical data in support of the theoretical results obtained in the context of non-relativistic domain. We analyze the pole structure of the quantum momentum function for the H2 molecule in the ground electronic state interacting with Kratzer oscillator in hyperspherical coordinates. Numerical results reveal clearly that moving poles of the quantum momentum function depend on nodes in the hyperradial wave function of related molecule. We also discuss in detail the influence of dimensions on the quantum momentum function.Öğe Analysis of quantum systems subject to inverse trigonometry Scarf plus Coulomb potential in N-dimensions(Iop Publishing Ltd, 2023) Ozfidan, AyselWe present approximate solutions of the N-dimensional Klein-Gordon equation in the presence of a superposition of inverse trigonometry Scarf potential and Coulomb potential through asymptotic iteration approach. With the purpose of dealing with the lN-1 -state, we use Greene-Aldrich approximation which is valid for the small values of the screening parameter. The analytical expressions for the relativistic energy eigenvalues and the corresponding eigenfunctions are established in hyperspherical coordinates. The normalized hyper-radial wavefunction is expressed in terms of hypergeometric and Jacobi polynomials. We analyze the dependences of the relativistic energy levels on the dimensions. We also discuss the effect of the screening parameter on the relativistic energy spectrum. The expectation values of inverse position r-1, the square of inverse position r-2, kinetic energy T and square of momentum p2 in N-dimensional space are reported using the Hellmann-Feynmann theorem. Discussing the special cases of the relevant potential, we show the accuracy of our results.Öğe Approximate Bound State Solutions of the Hellmann Plus Kratzer Potential in N-dimensional Space(Gazi Univ, 2020) Ozfidan, AyselWe have examined the approximate l(N-1)-state solutions of the N-dimensional Schrodinger equation for a particle interacting with the Hellmann plus Kratzer potential. In hyperspherical coordinate system, we have constructed the bound state energy equation and the wavefunctions expressed by the hypergeometric function via the asymptotic iteration approach in detail. When considered the special cases of parameters in Hellmann plus Kratzer potential, this potential turns into several potential models. In this connection, the non-relativistic energy spectra for the modified Kratzer, Yukawa, Coulomb and Hellmann potentials in approximate analytic form have been obtained in hyperspherical coordinates. We have presented the numerical energy eigenvalues for the Hellmann, Yukawa and Coulomb potentials in N = 3 dimensions. Our present results provide an appropriate test of the accuracy of asymptotic iteration formalism.Öğe Energy spectrum and applications of Eckart plus Hellmann potential in hyperspherical coordinates(Elsevier, 2024) Ozfidan, AyselWe investigate the approximate bound-state solutions of the N-dimensional Schro center dot dinger equation with a combination of Eckart and Hellmann potentials via the asymptotic iteration approach. By the use of the Greene-Aldrich approximation, which is valid for small values of the screening parameter, we establish the N-dimensional energy spectrum and the N-dimensional radial wave function in approximate analytic form. In hyperspherical coordinates, the normalized radial wave function is expressed in terms of hypergeometric and Jacobi polynomials. To double-check the energy spectrum in hyperspherical coordinates, we utilize polynomial solutions in view of the asymptotic iteration approach. The expressions for the expectation values of inverse position, square of inverse position, kinetic energy, and square of momentum are derived in hyperspherical coordinates by using the Hellmann-Feynmann theorem. We also present the analytically calculated energy eigenvalues for Eckart plus Hellmann potential. We deduce special forms of the relevant potential, such as Eckart, Hellmann, and Hulthe ' n potentials.Öğe Four pseudo-mirror nuclei in the left-lower part of the nuclear chart(Elsevier, 2022) Kumar, Pawan; Gautam, Ratindra; Aydin, Sezgin; Ozfidan, AyselIn the present work, we have reported four new pseudo-mirror nuclei Fe-64-Zn-70 and Cr-60-Ge-74. We have discussed the symmetry in their ground state energy band and kinematic moment of inertia. Further, we have discussed the pseudo-spin coupling in the view of pseudo-mirror nuclei. (C) 2022 Elsevier B.V. All rights reserved.Öğe Quantum pseudo-harmonic oscillator potential in non-Euclidean space: application to diatomic molecules(Iop Publishing Ltd, 2025) Ozfidan, AyselThe present work analyzes a physical system with a quantum pseudo-harmonic oscillator in three-dimensional constant curvature spaces within the framework of non-relativistic theory. We present expressions for the energy equation and radial wavefunctions that depend on the curvature parameter kappa, using the functional analysis approach and the asymptotic iteration method. Additionally, we calculate the energy eigenvalues for diatomic molecules N2, H2, and ScH as a function of the constant curvature kappa. Using the Hellmann-Feynmann theorem, we derive expressions for the curvature-dependent expectation values of r-2 and p2, which we detail for the diatomic molecule system in this work. Furthermore, we perform a comparative analysis of the results for non-Euclidean space (spherical and hyperbolic spaces with constant curvature) and Euclidean space.Öğe Relativistic treatment of alkaline earth dimers in the presence of non-central molecular potential in N-dimensions(Elsevier, 2021) Durmus, Aysen; Ozfidan, AyselWithin the framework of relativistic theory, N-dimensional non-central Morse potential as anharmonic model is considered thoroughly to describe the internuclear motion of alkaline earth dimers in the different electronic states. We illustrate the surface plots of alkaline earth dimers to examine the effect of angular potential, due to existence of molecular systems in which spherical symmetry disappears. Also, the contribution of angle dependent interaction to the relativistic energy spectra has been investigated in N-dimensions. We determine the relativistic vibrational transition frequencies in the lower vibrational states for the X-1 Sigma(+)(g) ground state of Mg-24(2), Ca-40(2), (MgCa)-Mg-24-Ca-40 and A(1)Sigma(+)(u) excited state of Sr-88(2) alkaline earth diatomic molecules. The theoretical results have been compared with Rydberg-Klein-Rees (RKR) and the inverted perturbation approach (IPA) experimental data. We also discussed the validity of Pekeris approximation around the equilibrium distance as well as the repulsive and attractive regions for alkaline earth dimers.Öğe Spin Symmetric Solutions in Central Field Including Tensor Interaction(Springer Wien, 2023) Ozfidan, AyselFor any spin-orbit quantum number k, we present the bound state solutions of the Dirac equation with Hulthen plus a class of Yukawa potential in the presence of a Coulomb-like tensor interaction under spin symmetry limit. We construct relativistic energy spectrum and the radial wavefunction by means of asymptotic iteration approach in approximate analytic form. By applying a developed scheme which is based on Greene Aldrich approximation, we cope with the centrifugal term. We investigate the effect of tensor potential on spin doublets. We report special cases of a combination of Hulthen potential and a class of Yukawa potential such as Hulthen, Yukawa, inversely quadratic Yukawa potentials.
