Related papers: T-matrix in discrete oscillator representation
Motivated by recently developed techniques making it possible to compute Casimir energies for any object whose scattering S-matrix (or, equivalently, T-matrix) is available, we develop a variable phase method to compute the S-matrix for…
A set of 13 linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle is derived which respect Lorentz and gauge invariance. The $T$-matrix can be represented by a…
We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\mathbb{E}_{3}$ where the potential is singular but invariant under…
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…
The fully discrete problem for convection-diffusion equation is considered. It comprises compact approximations for spatial discretization, and Crank-Nicolson scheme for temporal discretization. The expressions for the entries of inverse of…
We perform a 1-parameter family of self-adjoint extensions characterized by the parameter $\omega_0$. This allows us to get generic boundary conditions for the quantum oscillator on $N$ dimensional complex projective space($\mathbb{C}P^N$)…
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of…
The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional…
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…
We solve the loop equations to all orders in $1/N^2$, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for…
Suitable complexification of the well known solvable oscillators in one dimension is shown to give the four exactly solvable models which combine the shape- and PT-invariance. In version v2 the result is extended of the s-wave…
Given a Hilbert space operator $T$, the level sets of function $\Psi_T(z)=\|(T-z)^{-1}\|^{-1}$ determine the so-called pseudospectra of $T$. We set $\Psi_T$ to be zero on the spectrum of $T$. After giving some elementary properties of…
We study the generalized harmonic oscillator which has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for…
Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…
We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and…
The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures…