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Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain the two-point Green's function of the relativistic Dirac-Morse problem. This is accomplished by setting up the…
An analytical solution of the Dirac equation with a Cornell potential, with identical scalar and vectorial parts, is presented. The solution is obtained by using the linear potential solution, related to Airy functions, multiplied by…
Motivated by the discovery of superconductivity in beta-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
Motivated by recent experimental refinements of stellar reaction rates, we establish a non-perturbative Green's function formalism based on the exact solution of the Dyson equation for sub-barrier proton-nucleus resonant scattering. By…
Energy-dependent Green's functions for the two and three dimensional $\delta$-function plus harmonic oscillator potential systems are derived by incorporating the renormalization and the self-adjoint extension into the Green's function…
We propose an analytical method for finding the time domain solution for the problem of electronic relaxation of a molecule in solution. The relaxation process is modeled by the decay of a diffusing probability distribution through an…
We present a simple exact analytical solution, using the Weyl-Titchmarsh-Kodaira spectral theorem, for the spectral function of the one-dimensional diatomic molecule model consisting of two attractive delta function wells in the presence of…
A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation…
In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the…
The present work develops a rigorous framework for collective dipole oscillations in dense dielectric media by extending the Lorentz oscillator model to include both quadratic (second order) and cubic (third order) nonlinear restoring…
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined.…
Microscopic calculations of the electromagnetic response of medium-mass nuclei are now feasible thanks to the availability of realistic nuclear interactions with accurate saturation and spectroscopic properties, and the development of…
In the application of potential models, the use of the Dirac equation in central potentials remains of phenomenological interest. The associated set of decoupled second-order ordinary differential equations is here studied by exploiting the…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…