Related papers: Algebraic treatment of the confluent Natanzon pote…
We study a class of exactly solvable models for strongly correlated electrons, defined on a set of N cells, and with infinite on-site repulsion on part of the sites of each cell. For 2N or more electrons the exact ground state is known. We…
A completely algebraic treatment of the six-dimensional hypercoulomb problem is discussed in terms of an oscillator realization of the dynamical algebra of SO(7,2). Closed expressions are derived for the energy spectrum and form factors.
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the…
New approximate analytical solutions have been obtained for the conformable fractional collective Bohr Hamiltonian suitable for triaxial nuclei, with the harmonic oscillator in {\gamma}-part of the collective potential and different…
A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…
It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states by closing the boundary bootstrap and gave a derivation of Al.B.…
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are…
Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The…
We use a two-fluid model combining the quantum Green's function technique for the electrons and a classical HNC description for the ions to calculate the high-density equation of state of hydrogen. This approach allows us to describe fully…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along…
Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is…
A recently developed three-dimensional approach (without partial-wave decomposition) is considered to investigate solutions of Faddeev-Yakubovsky integral equations in momentum space for three- and four-body bound states, with the inclusion…
The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from…
The mean-square width of the energy profile of bosonic string is calculated considering two boundary terms in the effective action. The perturbative expansion of the Lorentz-invariant boundary terms at the second and the fourth order in the…
We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit…
A new expansion is established for the Green's function of the electromagnetic field in a medium with arbitrary $\epsilon$ and $\mu$. The obtained Born series are shown to consist of two types of interactions - the usual terms (denoted…
We introduce some new classes of algebras and estabilish in these algebras Campbell--Hausdorff like formula. We describe the application of these constructions to the problem of the connectivity of the Feynman graphs corresponding to the…
An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…