Related papers: Jost function formalism with complex potential
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…
Light front formalism for composite systems is presented. Derivation of equations for bound state and scattering problems are given. Methods of constructing of elastic form factors and scattering amplitudes of composite particles are…
In a recent paper a class of infinite Jacobi matrices with discrete character of spectra has been introduced. With each Jacobi matrix from this class an analytic function is associated, called the characteristic function, whose zero set…
We develop a method to construct a microscopic optical potential from chiral interactions for nucleon-nucleus scattering. The optical potential is constructed by combining the Green's function approach with the coupled-cluster method. To…
It is shown that an application of optical theorem for the non-unitary S-matrix can lead to the qualitative error in the result.
In this paper we extend the applicability of Fox-Wright functions beyond mathematics, specifically in quantum physics. We focused our attention on a new application, on the connection between the Fox-Wright functions and the generalized…
We study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications.
One-dimensional $\delta^{'}$-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent…
Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. In this article, squared eigenfunctions are derived for the Sasa-Satsuma…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
The matrix elements of the multi-channel Jost matrices are written in such a way that their dependencies on all possible odd powers of channel momenta are factorized explicitly. As a result the branching of the Riemann energy surface at all…
We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressions for realization of a regular product of rational…
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly…
We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…