The generalized pseudospectral approach to the bound states of Hulthen and Yukawa potentials (original) (raw)
Related papers
The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials
Pramana, 2005
The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a non-uniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with n ≤ 10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as n = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n > 6 states of the Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of the Yukawa potential, the present method surpasses the accuracy of all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.
Atomic and molecular bound ground states of the Yukawa potential
Physical Review A, 1997
The variational self-consistent field molecular-orbital method is used to compute both atomic and molecular full configuration interaction ͑FCI͒ energies of the hydrogen anion and the hydrogen molecule, for the Yukawa potential. The spin orbitals have been expanded as linear combinations of Gaussian basis functions, for which complete analytical formulas for all the required basic integrals are available. Both the ionization potential of the hydrogen anion and the behavior of the molecular properties of the hydrogen molecule have been analyzed in detail with extensive basis sets at the FCI level of theory. Finally, the growing importance of the electron correlation energy as the screening parameter increases has been demonstrated clearly by our calculations.
Accurate calculation of the bound states of Hellmann potential
Journal of Mathematical Chemistry, 2008
Bound states of the Hellmann potential, which is a superposition of the attractive Coulomb (−A/r) and the Yukawa (Be −Cr /r) potential, are calculated by using a generalized pseudospectral method. Energy eigenvalues accurate up to thirteen to fourteen significant figures, and densities are obtained through a nonuniform, optimal spatial discretization of the radial Schrödinger equation. Both ground and excited states are reported for arbitrary values of the potential parameters covering a wide range of interaction. Calculations have been made for higher states as well as for stronger couplings. Some new states are reported here for the first time, which could be useful for future works. The present results are significantly improved in accuracy over all other existing literature values and offers a simple, accurate and efficient scheme for these and other singular potentials in quantum mechanics.
Studies on some exponential-screened coulomb potentials
International Journal of Quantum Chemistry, 2013
The generalized pseudospectral method is employed to study the bound-state spectra of some of the exponentially screened Coulomb potentials, viz., the exponential cosine screened Coulomb (ECSC) and general exponential screened Coulomb (GESC) potential, with special emphasis on higher states and stronger interaction. Eigenvalues accurate up to eleven significant figures are obtained through a non-uniform optimal spatial discretization of the radial Schrödinger equation.
The solutions of the Schrödinger with more general exponential screened coulomb (MGESC), Yukawa potential (YP) and the sum of the mixed potential (MGESCY) have been presented using the Parametric Nikiforov-Uvarov Method (pNUM). The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions expressed in terms of hypergeometric functions were obtained. Some derived equations were used to calculate numerical values for MGESC, YP, and MGESCY potentials for diatomic molecules with different screening parameters (α) for l = 0 and l = 1 state with V 0 = 2.75 MeV and V 1 = 2.075 MeV. We observed an increase in l value; the particles behave more repulsive than attractive. The numerical values for different l-states at different screening parameters for CO molecules (r = 1.21282) and NO molecule (r = 1.1508) were obtained using the bound state energy eigenvalue of the Schrodinger equation for MGESC, YP and MGESCY potentials. Potential variation with intermolecular distance (r) for some of the particles moving under the influence of MGESC, Yukawa and the mixed potential (MGESCY) were also studied. We also observed the variation of the MGESC potential How to cite this paper: Ita,
2019
Considering the stationary Schrödinger equation for a general pseudo-Coulomb potential as the normal form of the associated Laguerre equation, we review, in one and three dimensions, the bound-state solutions for the potential, when the inverse-square-term coupling is not less than a negative critical value. We show that, as a consequence of the inverse-square-term coupling being a two-to-one mapping for all but one of the allowed negative values of its parameter, an additional sequence of bound-state energies emerges for each of the respective potentials. In this framework, the slightest relaxation of the boundary condition for the radial wave function at the origin results in minus-infinity ground-state energy for the Coulomb potential, rendering the hydrogen atom unstable. The article has been published in the journal "New Horizons in Mathematical Physics", Vol. 3, No. 4, December 2019. Available at: https://dx.doi.org/10.22606/nhmp.2019.34001
Journal of Molecular Modeling
We have obtained analytically the bound state solutions for the non-relativistic Schrodinger equation for the Eckart plus inversely quadratic Yukawa potential (EIQYP) using the parametric Nikiforov-Uvarov (NU) method. In order to validate our approximation, the bound state energies were computed and predicted for some selected diatomic molecules at different adjustable screening parameters from the available spectroscopic model parameters. The fact-finding obtained are in agreement with previously reported results available in literature. Furthermore, the graphs of the effective potential against inter-nuclear distance for low and high values of the screening parameters were reported. From our graphs, we observed that the approximation is best fit for very low values of the screening parameter α ≪ 1.
Eigensolutions, scattering phase shift and thermodynamic properties of Hulthẻn-Yukawa potential
Results in physics, 2019
Petiau wave equation is highly recommendable. Thus, the approximate bound state of the Duffin-Kemmer-Petiau equation and Schrӧdinger equation were obtained with a combination of Hulthẻn and Yukawa potentials in the framework of asymptotic iteration method and parametric Nikiforov-Uvarov method respectively for any arbitrary angular momentum quantum number J using a suitable approximate scheme to the centrifugal term. This was done when the second-order homogeneous differential equation was transformed to a form of recurrence relation from which a quantization condition obtained was used to calculate the eigenvalue energy equation and the corresponding wave function. In other to apply more application to this work, the scattering phase shift of the Duffin-Kemmer-Petiau equation was calculated and the thermodynamic properties of the potential under consideration were also calculated in view of the Schrӧdinger equation. It is noted that the results obtained by varying the two strengths of the potential differs due to the effect of the screening parameter.
International Journal of Quantum Chemistry, 2004
The coupled Schrö dinger equation for three-body atomic systems such as Ps Ϫ (e ϩ e Ϫ e Ϫ), Mu(ϩ e Ϫ e Ϫ), p ϩ Ϫ Ϫ , d ϩ Ϫ Ϫ , and t ϩ Ϫ Ϫ is solved by using the hyperspherical harmonic-generalized Laguerre polynomial expansion method (HHGLP). Ground-state eigenenergies are calculated for the certain number of basis functions. The eigenenergies of the first excited states are obtained for both pure Coulomb, V(r, ⍀) ϭ Ẑ (⍀)/r, and Fues-Kratzer-type (FK-type) potential, V(r, ⍀) ϭ Ẑ (⍀)/r ϩ Â (⍀)/r 2. As an example, to illustrate the effect of FK-type interaction on the lowest excited states, the eigenenergies of the Mu Ϫ ion are given together as a function of the certain number of basis functions for both potentials. Our results were compared with the other theoretical calculations. Ground-state eigenenergies of atoms such as X ϩ Y Ϫ Y Ϫ as a function of the reduced mass were investigated. The potential curves of the ground and first excited states of Ps Ϫ (e ϩ e Ϫ e Ϫ), Mu Ϫ (ϩ e Ϫ e Ϫ), p ϩ Ϫ Ϫ systems were obtained by a diagonalization process. It is pointed out that the FK-type potential makes the HH method more useful and more extended for atomic calculations.