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The strong electron correlations caused by Coulomb interaction of impurity electrons are taken into account. The infinite series of diagrams containing irreducible Green's functions are summed. For symmetric Anderson model we establish the…
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized…
Using the decay along the diagonal of the matrix representing the perturbation with respect to the Hermite basis, we prove a reducibility result in $L^2(\mathbb{R})$ for the one-dimensional quantum harmonic oscillator perturbed by time…
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…
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…
We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…
We study the interaction of a scalar and a spinning particle with a coherent linearized gravitational wave field treated as a classical spin two external field. The spin degrees of freedom of the spinning particle are described by…
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the…
Studying the problem of wave propagation in media with resistive boundaries can be made by searching for "resonance modes" or free oscillations regimes. In the present article, a simple case is investigated, which allows one to enlighten…
We establish the relation between full traces of the Green functions for some initial and the Darboux transformed one-dimensional two component Dirac problems with the most general form of potential. The result is used to check the…
The sextic oscillator is proposed as a two-parameter solvable $\gamma$-independent potential in the Bohr Hamiltonian. It is shown that closed analytical expressions can be derived for the energies and wavefunctions of the first few levels…
We derive boundary conditions for electromagnetic fields on a $\delta$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We…
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…
We study the linear phenomenological Maxwell's equations in the presence of a polarizable and magnetizable medium (magnetodielectric). For a dispersive, non-absorptive, medium with equal electric and magnetic permeabilities, the latter can…
We develop a formalism to extend our previous work on the electromagnetic $\delta$-function plates to a spherical surface. The electric ($\lambda_e$) and magnetic ($\lambda_g$) couplings to the surface are through $\delta$-function…
We observe a resonance in the conductance of silicon tunneling devices with a delta-doped barrier. The position of the resonance indicates that it arises from tunneling through the B^+ state of the boron atoms of the delta-layer. Since the…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the…
We discuss the notion of resonance, as well as the existence and uniqueness of periodic solutions for a forced simple harmonic oscillator. While this topic is elementary, and well-studied for sinusoidal forcing, this does not seem to be the…
We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average…