21 citations · 106 across the 24 of their papers we have counts for
24 papers
Highly accurate potential energy curves for the hydrogen molecule ion
Francisco Marcelo Fernández, Javier Garcia
Potential energy surfaces of the hydrogen molecular ion H in the Born-Oppenheimer approximation are computed by means of the Riccati-Padé method (RPM). The convergence proper…
On the Majorana solution to the Thomas-Fermi equation
Francisco M. Fernández, Javier Garcia
We analyse the solution to the Thomas-Fermi equation discovered by Majorana. We show that the series for the slope at origin enables one to obtain results of accuracy far beyond th…
Nonlinear effects on the dynamics of quantum harmonic modes coupled through angular momentum
N. Canosa, R. Rossignoli, Javier Garcia +2
We investigate nonlinear effects on the dynamics of entanglement and other quantum observables in a system of two harmonic modes coupled through angular momentum. The nonlinearity…
Statistics of the Eigenvalues of a Noisy Multi-Soliton Pulse
Javier Garcia, Vahid Aref
For Nonlinear-Frequency Division-Multiplexed (NFDM) systems, the statistics of the received nonlinear spectrum in the presence of additive white Gaussian noise (AWGN) is an open pr…
Spectrum and normal modes of non-hermitian quadratic boson operators
Javier Garcia, R. Rossignoli
We analyze the spectrum and normal mode representation of general quadratic bosonic forms not necessarily hermitian. It is shown that in the one-dimensional case such forms exh…
On two different kinds of resonances in one-dimensional quantum-mechanical models
Francisco M. Fernández, Javier Garcia
We apply the Riccati-Padé method and the Rayleigh-Ritz method with complex rotation to the study of the resonances of a one-dimensional well with two barriers. The model exhibits t…
Three PT-symmetric Hamiltonians with completely different spectra
Francisco M. Fernández, Javier Garcia
We discuss three Hamiltonians, each with a central-field part and a PT-symmetric perturbation . When is the isotropic Harmonic oscillator the spectrum is real…
Highly accurate calculation of the resonances in the Stark effect in hydrogen
Francisco M Fernández, Javier Garcia
We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonaliza…
On recent calculations of resonances for the Stark effect in hydrogen
Francisco M. Fernández, Javier Garcia
We show that the resonances of the Stark effect in hydrogen reported in Phys. Rev. A \textbf{88}, 022509 (2013) are considerably less accurate than the number of digits appear to s…
Unitary transformations of a family of two-dimensional anharmonic oscillators
Francisco M. Fernández, Javier Garcia
In this paper we analyze a recent application of perturbation theory by the moment method to a family of two-dimensional anharmonic oscillators. By means of straightforward unitary…
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…
Ad hoc physical Hilbert spaces in Quantum Mechanics
Francisco M. Fernández, Javier Garcia, Iveta Semorádová +1
The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an ele…
On the eigenvalues of some non-Hermitian Hamiltonians with space-time symmetry
Paolo Amore, Francisco M. Fernández, Javier Garcia
We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in…
Comparison of two semiclassical expansions for a family of PT-symmetric oscillators
Francisco M. Fernández, Javier Garcia
We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form does not agree with an earlier WKB expr…
Eigenvalues and eigenfunctions of the anharmonic oscillator
Francisco M. Fernández, Javier Garcia
We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential by means of three different methods. Our results str…
PT-symmetry broken by point-group symmetry
Francisco M Fernández, Javier Garcia
We discuss a PT-symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential…
Non-hermitean hamiltonians with unitary and antiunitary symmetry
Francisco M. Fernández, Javier Garcia
We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy…
Rayleigh-Ritz variational method with suitable asymptotic behaviour
Javier Garcia, Francisco M Fernández
We discuss Rayleigh-Ritz variational calculations with nonorthogonal basis sets that exhibit the correct asymptotic behaviour. We construct the suitable basis sets for general one-…
-symmetric strings
Paolo Amore, Francisco M. Fernández, Javier Garcia +1
We study both analytically and numerically the spectrum of inhomogeneous strings with -symmetric density. We discuss an exactly solvable model of -symme…
Critical parameters for non-hermitian Hamiltonians
Francisco M Fernández, Javier Garcia
We calculate accurate critical parameters for a class of non-hermitian Hamiltonians by means of the diagonalization method. We study three one-dimensional models and two perturbed…
On the eigenvalues of some nonhermitian oscillators
Francisco M. Fern/'andez, Javier Garcia
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by…
Local approximation to the critical parameters of quantum wells
Francisco M. Fernández, Javier Garcia
We calculate the critical parameters for some simple quantum wells by means of the Riccati-Padé method. The original approach converges reasonably well for nonzero angular-momentum…
Comment on: 'A simple analytical expression for bound state energies for an attractive Gaussian confining potential'
Francisco M Fernández, Javier Garcia
We discuss a recently proposed analytical formula for the eigenvalues of the Gaussian well and compare it with the analytical expression provided by the variational method with the…