6 citations · 23 across the 22 of their papers we have counts for
11 papers · 2 filters
On the effective secular equation
Francisco M. Fernández
We show that the effective secular equation proposed several years ago is suitable for estimating the location of the exceptional points of eigenvalue equations. As an illustrative…
Algebraic analysis of non-Hermitian quadratic Hamiltonians
Francisco M. Fernández
We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit -symmetry. By means of an algebraic method we determine the conditions for the e…
On the interaction of a magnetic quadrupole moment with an electric field in a rotating frame
Francisco M. Fernández
We discuss results obtained recently for a quantum-mechanical model given by a neutral particle with a magnetic quadrupole moment in a radial electric field and a scalar potential…
On the problem of the vanishing discriminant
Francisco M. Fernández
We show that the straightforward application of the discriminant to some physical problems may yield a trivial useless result. If the symmetry of the model matrix does not change w…
On the application of the Adomian-based methods
Francisco M. Fernández
We analyze a recent application of two Adomian-based approximate methods to the Chen-Lee-Liu equation. We prove that the outcome of these approaches is merely the Taylor expansion…
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…
Extremely broken generalized symmetry
Francisco M. Fernández
We discuss some simple Hückel-like matrix representations of non-Hermitian operators with antiunitary symmetries that include generalized (parity transformation foll…
On the Rayleigh-Ritz variational method
Francisco M. Fernández
We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz variational method are increasingly accurate upper bounds to the exact…
On the misinterpretation of conditionally-solvable quantum-mechanical problems
Francisco M. Fernández
We apply the Frobenius (power-series) method to some simple exactly-solvable and conditionally-solvable quantum-mechanical models with supposed physical interest. We show that the…
On the Q-BOR-FDTD method
Francisco M. Fernández
We discuss a recently proposed approach termed Q-BOR-FDTD method and develop its main equations in a clearer and more rigorous way. We show that it is unsuitable for the calculatio…
Alternative solution to a quantum-mechanical four-particle system in one dimension
Francisco M. Fernández
We propose an alternative solution to a quantum-mechanical four-particle system in one dimension with two- and three-particle interactions. The solution of the eigenvalue equation…