7 citations · 7 across the 16 of their papers we have counts for
16 papers
On some potentials based on exponential functions
Francisco M. Fernández
By means of a simple and systematic normalization method we show that some apparently different potentials based on exponential functions are equivalent. Present normalization meth…
On solutions of the Schrödinger equation for some molecular potentials: Power-series method
Francisco M. Fernández
We show that the standard power-series method described in many textbooks of quantum-mechanics and quantum-chemistry is simpler and more powerful than the wavefunction approach pro…
Exact solutions, critical parameters and accidental degeneracy for the hydrogen atom in a spherical box
Francisco M. Fernández
We derive some properties of the hydrogen atom inside a box with an impenetrable wall that have not been discussed before. Suitable scaling of the Hamiltonian operator proves to be…
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…
On the application of the Rayleigh-Ritz method to a projected Hamiltonian
Francisco M. Fernández
We apply the well known Rayleigh-Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh-Ritz variational principle to ensem…
On the exact solutions of a one-dimensional Schrödinger equation with a rational potential
Francisco M. Fernández
We analyse the exact solutions of a conditionally-solvable Schrödinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between…
Just another conditionally-solvable non-relativistic quantum-mechanical model
Francisco M. Fernández
We show that a perturbed Coulomb problem discussed recently is conditionally solvable. We obtain the exact eigenvalues and eigenfunctions and compare the former with eigenvalues ca…
On the two-dimensional harmonic oscillator with an electric field confined to a circular box
Francisco M. Fernández, Javier Garcia, Norberto Aquino +1
We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectru…
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 screened Kratzer potential and its variants
Francisco M. Fernández
We argue that several potentials proposed recently for the analysis of the vibrational-rotational spectra of diatomic molecules and their thermodynamic properties exhibit a flaw. O…
On the Raleigh-Ritz variational method. Non-orthogonal basis set
Francisco M. Fernández
We overview the main equations of the Rayleigh-Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.
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…
On the spectrum of the screened Coulomb potential
Francisco M. Fernández
We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential . The well known Hellmann-Feynman theorem shows t…
On the variational treatment of a class of double-well oscillators
Francisco M. Fernández, Javier Garcia
We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization…
On the normal modes of coupled harmonic oscillators
Francisco M. Fernández
We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two…
Comment on: "Harmonic oscillator in an environment with a pointlike defect". Phys. Scr. \textbf{94} ( 2019) 125301
Francisco M. Fernández
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a…