arXiv subjects
Publications and source records attributed to Francisco M. Fernández.
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustrative examples.
We analyze a simple textbook approach to nonlinear oscillators proposed recently, disclose its errors, limitations and misconceptions and complete the calculations that the authors failed to perform.
We review some of the few available nonadiabatic calculations of dipole moments. We show that those carried out in a laboratory-fixed set of coordinate axes are bound to fail and discuss the more reasonable ones in a molecule-fixed reference frame. For completeness we also describe the standard Born--Oppenheimer calculations of dipole moments. We briefly address the experimental estimation of dipole moments from the Stark shift of spectral lines and argue that it does not provide such property but a sort of energy--weighted average of dipole transition moments.
We argue that the dynamic extended molecular orbital (DEMO) method may be less accurate than expected because the motion of the center of mass was not properly removed prior to the SCF calculation. Under such conditions the virial theorem is a misleading indication of the accuracy of the wavefunction.
We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the time variable. We derive more general results by means of travelling waves and argue that a curious superposition principle may not be of any mathematical or physical significance.
In this letter we analyse an amazing variational approach to chemical reactions. Our results clearly show that the variational expressions are unsuitable for the analysis of empirical data obtained from chemical reactions.
We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.
In this comment we point out some wrong statements in the paper by Inc and Cavlak, Phys. Scr. 78 (2008) 045008
I discuss a recent application of homotopy perturbation and Adomian decomposition methods to the linear and nonlinear Schrödinger equations. I propose a generalization of the procedure for the treatment of a wider class of problems.
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it provides solutions to both the bounded and unbounded type of models simultaneously
The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang--big crunch) at the quantum level. We show that a proper study of their model{\sl does not prevent} the occurrence of singularities at the quantum level, in fact the quantum probability of such event is larger than the classical one. Our numerical simulations based on the powerful variational sinc collocation method (VSCM) also show that the precision of the results of that paper is much lower than the 20 significant digits reported by the authors.
In this paper we study a new family of sinc--like functions, defined on an interval of finite width. These functions, which we call ``little sinc'', are orthogonal and share many of the properties of the sinc functions. We show that the little sinc functions supplemented with a variational approach enable one to obtain accurate results for a variety of problems. We apply them to the interpolation of functions on finite domain and to the solution of the Schrödinger equation, and compare the performance of present approach with others.