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Francisco M. Fernández

Publications and source records attributed to Francisco M. Fernández.

At least 163 records · Page 9Linked to original sources
arXiv2011

Comment on: "Non-relativistic treatment of diatomic molecules interacting with generalized Kratzer potential in hyperspherical coordinates"

We argue that the textbook method for solving eigenvalue equations is simpler, more elegant and efficient than the Asymptotic Iteration Method (AIM) applied in J. Phys. A {\bf 44} 155205. We show that the Kratzer potential is not a realistic model for the vibration--rotation spectrua of diatomic molecules because it predicts the position of the absorption infrared bands too far from the experimental ones (at least for the $HCl$ and $H_2$ molecules chosen as illustrative examples in that paper).

quant-ph↗
arXiv2011

On certain sum rules for the hydrogen atom

We show that some sum rules for the hydrogen atom derived recently are incorrect because the authors did not take into account the continuous part of the spectrum in the sum over intermediate states.

math-ph↗
arXiv2011

Wronskian method for bound states

We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider an exactly solvable model and the Gaussian potential well.

quant-ph↗
arXiv2011

Quantum scattering by Wronskians

We show that Wronskians between properly chosen linearly independent solutions of the Schrödinger equation greatly facilitate the study of quantum scattering in one dimension. They enable one to obtain the necessary relationships between the coefficients that determine the asymptotic behavior of the wavefunction. As illustrative examples we calculate the transmission probability for the penetration of a Gaussian barrier and the scattering resonances for a Gaussian well.

quant-ph↗
arXiv2010

High--order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large--order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.

quant-ph↗
arXiv2010

Variational and perturbative approaches to the confined hydrogen atom with a moving nucleus

We calculate the ground--state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and perturbation theory and compare both approximate results. We show that the total, kinetic and potential energies for the moving--nucleus model are greater than those for the case in which the nucleus is clamped at the box center.

quant-ph↗
arXiv2010

Perturbation theory for confined systems

We discuss the application of perturbation theory to a system of particles confined in a spherical box. A simple argument shows that the particles behave almost independently in sufficiently strong confinement. We choose the helium atom with a moving nucleus as a particular example and compare results of first order with those for the nucleus clamped at the center of the box. We provide a suitable explanation for some numerical results obtained recently by other authors.

quant-ph↗
arXiv2010

Simple one-dimensional quantum-mechanical model for a particle attached to a surface

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. We solve the Schrödinger equation in terms of Weber functions and discuss the behavior of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(100) and also outline the application of the Rayleigh-Ritz variational method.

quant-ph↗
arXiv2010

Accurate calculation of resonances for a central-field model potential

We obtain accurate resonance energies for the Schrödinger equation with a central--field potential by means of a method based on a rational approximation to the logarithmic derivative of the wavefunction. We discuss the rate of convergence of our approach and compare present results with those obtained earlier by other authors. We show that present method is superior to the spherical--box approach applied recently to the same problem. As far as we know present results are more accurate than those available in the literature and may be a suitable benchmark for testing future approaches.

math-ph↗
arXiv2009

HAM and HPM: Another attack to reason

We discuss two recent applications of homotopy analysis method and homotopy perturbation method and conclude that the results are completely useless from both mathematical and physical points of view.

math-ph↗
arXiv2009

Collocation method for fractional quantum mechanics

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on Little Sinc Functions (LSF), which discretizes the Schrödinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a WKB analysis is performed.

quant-ph↗
arXiv2009

Nonsensical models for quantum dots

We analyze a model proposed recently for the calculation of the energy of an exciton in a quantum dot and show that the authors made a serious mistake in the solution to the Schrödinger equation.

math-ph↗
arXiv2009

More integrals of products of Airy functions

By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.

math-ph↗
arXiv2009

On a perturbation treatment of a model for MHD viscous flow

We discuss the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet. We propose an accurate numerical solution and derive simple analytical expressions. Our results suggest that a recent perturbation treatment of the same problem exhibits a pathological behaviour and conjecture its probable cause.

math-ph↗