On the homotopy perturbation method for Boussinesq-like equations

We comment on some analytical solutions to a class of Boussine sq-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 traveling waves and argue that a curious superposition principle proposed by the author may not be of any mathematical or physical significance.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentin

The Hellmann-Feynman theorem for statistical averages

We discuss the Hellmann-Feynman theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentin

On the homotopy perturbation method for Boussinesq-like equations

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 traveling waves and argue that a curious superposition principle proposed by the author may not be of any mathematical or physical significance.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

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.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Comment on “Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation” [J. Math. Phys. 59, 053501 (2018)]

We analyze some polynomial solutions to the Schrödinger equation with a central-field potential derived recently by means of the so-called extended Nikiforov-Uvarov method. We show that this approach does not produce the spectrum of the non-relativistic quantum-mechanical model but merely some eigenvalues for particular values of the model parameters. In addition, the approach just mentioned appears to overlook the restrictions that reveal the problem as conditionally solvable.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin

Accurate calculation of the eigenvalues of a new simple class of superpotentials in SUSY quantum mechanics

We obtain accurate eigenvalues for two recently derived SUSY partner Hamiltonians. We improve the Rayleigh-Ritz variational method proposed by the authors and show how to apply the Riccati-Padé method to those particular partner potentials.Facultad de Ciencias ExactasInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

On the crossing of the energy levels of a parameter-dependent quantum-mechanical Hamiltonian

The non-crossing rule for the energy levels of a parameter-dependent Hamiltonian is revisited and a flaw in a commonly accepted proof is revealed. Some aspects of avoided crossings are illustrated by means of simple models. One of them shows the close relationship between avoided crossings and exceptional points.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Comment on: "Spin-0 scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in 5 D cosmic string spacetime"

We show that the meaning of the eigenvalues of a radial equation derived from a powerseries method was misunderstood. The roots stemming from the truncation of the power series through a three-term recurrence relation are not the energies of the quantummechanical model under study but isolated particular eigenvalues of different models. The supposed dependence of the intensity of the magnetic field on the quantum numbers is just an artifact of the truncation method.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin

Comment on “He-Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics”

In this Comment we argue that the so-called He-Laplace variational iteration method merely yields the Taylor series of the solution to a partial differential equation. The straightforward application of the textbook power series method is far simpler and more efficient because it gives us closed-form analytic recurrence relations for the expansion coefficients. We also argue that the time series of the solution is unsuitable for the analysis of nonlinear problems in chemical kinetics and population dynamics which require expressions valid for sufficiently large time. Besides, Nadeem and He (J Math Chem 59:1234–1245, 2021) applied the approach to some tailor-made toy problems with known exact solutions that do not appear to exhibit any physical application whatsoever.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin