Related papers: All-coupling solution for the continuous polaron p…
Solutions of the Schr\"odinger equation by spanning the wave function is a complete basis is a common practice is many-body interacting systems. We shall study the case of a two-dimensional quantum system composed by two interacting…
We present an elementary proof based on a direct calculation of the property of completeness at constant time of the solutions of the Klein-Gordon equation for a charged particle in a plane wave electromagnetic field. We also review…
The strong coupling treatment of the Fr\"ohlich-type polaronic system, based on a canonical transformation and a standard Landau-Pekar type variational wave function, is applied to the polaronic system consisting of an impurity in a…
Exact solutions of effective radial Schr\"{o}dinger equation are obtained for some inverse potentials by using the point canonical transformation. The energy eigenvalues and the corresponding wave functions are calculated by using a set of…
Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…
For the Fr\"ohlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the Fr\"ohlich…
In this paper, we use the variational method, especially the perturbation method, to find the perturbed high energy solutions of the quadratic coupled Schrodinger system with asymmetric asymptotic potential and their asymptotic behavior as…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…
The commutators of the Poincar\'e group generators will be unchanged in form if a unitary transformation relates the free generators to the generators of an interacting relativistic theory. We test the concept of unitary transformations of…
We develop a theoretical and computational framework to study polarons in semiconductors and insulators from first principles. Our approach provides the formation energy, excitation energy, and wavefunction of both electron and hole…
We use both a perturbative Green's function analysis and standard perturbative quantum mechanics to calculate the decrease in energy and the effective mass for an electron interacting with acoustic phonons. The interaction is between the…
In this paper, we consider a general form of nonlinear Schr\"{o}dinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schr\"{o}dinger equation is identified by…
A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully…
It is shown fields that cannot be represented over one complex plane can be further decomposed for representation over multiple complex planes. This finding is demonstrated here by solving of the Schr\"{o}dinger equation for the hydrogen…
We obtain solutions to the coupled Schr\"odinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships…
A selfconsistent system of equations describing evolution of linear spherically symmetric perturbations in Fridmann world by an arbitrary equation of state is obtained. The perturbations singular part corresponding to massive particle-like…
Energy spectrum of a weak coupling polaron is considered in a cylindrical quantum dot. An analytical expression for the polaron energy shift is obtained using a modified pertubation theory.
In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself…
We expand the existing polaron response theory, expressed within the Mori-Zwanzig projection operator formalism applicable for the transfer of arbitrary energy and zero momentum, to the case of finite momentum exchange. A general formula is…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…