112 citations · 1.1k across the 124 of their papers we have counts for
46 papers · 1 filter
On the two-dimensional hydrogen atom in a circular box in the presence of an electric field
Paolo Amore, Francisco M. Fernández
We revisit the quantum-mechanical two-dimensional hydrogen atom with an electric field confined to a circular box of impenetrable wall. In order to obtain the energy spectrum we re…
The Hellmann-Feynman theorem and the spectrum of some Hamiltonian operators
Paolo Amore, Francisco M. Fernández
In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.
On the eigenvalues of the harmonic oscillator with a Gaussian perturbation
Paolo Amore, Francisco M. Fernández, Javier Garcia
We test the analytical expressions for the first two eigenvalues of the harmonic oscillator with a Gaussian perturbation proposed recently. Our numerical eigenvalues show that thos…
Quantum particles in a suddenly accelerating potential
Paolo Amore, Francisco M. Fernández, Jose Luis Valdez
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropri…
An ubiquitous three-term recurrence relation
Paolo Amore, Francisco M. Fernández
We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coeff…
Comment on: "Quantum aspects of the Lorentz symmetry violation on an electron in a nonuniform electric field'' Eur. Phys. J. Plus (2020) 135:623
Paolo Amore, Francisco M. Fernández
We analyze recent results concerning the hypothesis of a privileged direction in the space-time that is made by considering a background of the Lorentz symmetry violation determine…
Gross misinterpretation of a conditionally solvable eigenvalue equation
Paolo Amore, Francisco M. Fernández
We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coeff…
Comment on: "On the effects of the Lorentz symmetry violation yielded by a tensor field on the interaction of a scalar particle and a Coulomb-type field" Ann. Phys. 399 (2018) 117-123
Paolo Amore, Francisco M. Fernández
We analyze the eigenvalues and eigenfunctions stemming from a recent study of the interaction of a scalar particle with a Coulomb potential in the presence of a background of the v…
On some conditionally solvable quantum-mechanical problems
Paolo Amore, Francisco M. Fernández
We analyze two conditionally solvable quantum-mechanical models: a one-dimensional sextic oscillator and a perturbed Coulomb problem. Both lead to a three-term recurrence relation…
Comment on "Bidimensional bound states for charged polar nanoparticles''
Paolo Amore, Francisco M. Fernández
In a recent paper Castellanos-Jaramillo and Castellanos-Moreno proposed a simple quantum-mechanical model for an electron in the vicinity of an ionized nanostructure with a permane…
On the Hellmann-Feynman theorem in statistical mechanics
Paolo Amore, Francisco M. Fernández
In this paper we develop the Hellmann-Feynman theorem in statistical mechanics without resorting to the eigenvalues and eigenvectors of the Hamiltonian operator. Present approach d…
Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators
Paolo Amore, Francisco M. Fernández
We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is g…
Quantum particles in a suddenly moving localized potential
Miguel Ahumada-Centeno, Paolo Amore, Francisco M Fernández +1
We study the behavior of a quantum particle, trapped in localized potential, when the trapping potential starts suddenly to move with constant velocity. In one dimension we have re…
Comment to: "The quantum square well with moving boundaries: a numerical analysis"
Miguel Ahumada-Centeno, Paolo Amore, Francisco M Fernandez
In this comment we show that the approach presented by Fojón et al~\cite{Fojon10} is not as accurate as they claim. A straightforward calculation using the models considered buy th…
On a model for rotational tunneling with a -space-time symetric analog
Paolo Amore, Francisco M. Fernández
We analyze the simple model of a rigid rotor with symmetry and show that the use of parity simplifies considerably the calculation of its eigenvalues. We also consider a no…
Weakly (and not so weakly) bound states of a relativistic particle in one dimension
Paolo Amore, Francisco M. Fernández, Enrique Jimenez
We present the first exact calculation of the energy of the bound state of a one dimensional Dirac massive particle in weak short-range arbitrary potentials, using perturbation the…
The harmonic oscillator in a space with a screw dislocation
Paolo Amore, Francisco M. Fernández
We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain suffi…
A quantum-mechanical anharmonic oscillator with a most interesting spectrum
Paolo Amore, Francisco M. Fernández
We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter . The ground…
Perturbation theory for short-range weakly-attractive potentials in one dimension
Paolo Amore, Francisco M. Fernández
We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method…
On two perturbation series for short-range attractive potentials
Paolo Amore, Francisco M. Fernández
We compare two alternative expansions for finite attractive wells. One of them is known from long ago and is given in terms of powers of the strength parameter. The other one is ba…
On an approximation to the Schrödinger equation with the Hellmann potential
Paolo Amore, Francisco M. Fernández
We tried to determine the range of validity of a recently proposed modification of the Hellmann potential that leads to analytical eigenvalues and eigenfunctions. We discuss the di…
Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
Paolo Amore, Francisco M. Fernández
We generalize a recently proposed small-energy expansion for one-dimensional quantum-mechanical models. The original approach was devised to treat symmetric potentials and here we…
Non-Hermitian oscillators with symmetry
Paolo Amore, Francisco M. Fernández, Javier Garcia
We analyse some PT-symmetric oscillators with symmetry that depend on a potential parameter . We calculate the eigenvalues and eigenfunctions for each irreducible repres…
Is space-time symmetry a suitable generalization of parity-time symmetry?
Paolo Amore, Francisco M. Fernández, Javier Garcia
We discuss space-time symmetric Hamiltonian operators of the form , where is Hermitian and real. is invariant under the unitary operatio…