Related papers: Operator Transformations Between Exactly Solvable …
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the…
We study one-dimensional Schr\"odinger operators defined as closed operators that are exactly solvable in terms of the Gauss hypergeometric function. We allow the potentials to be complex. These operators fall into three groups. The first…
Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single…
We introduce a concept of the operator (non-commutative) projective line PH defined by a Hilbert space H and a symplectic structure on it. Points of PH are Lagrangian subspaces of H. If a particular Lagrangian subspace is fixed then we can…
We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=…
A transformation method is applied to the second order ordinary differential equation satisfied by orthogonal polynomials to construct a family of exactly solvable quantum systems in any arbitrary dimensional space. Using the properties of…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
We report some recent results on analytic pseudodifferential operators, also known as Wick operators. An important tool in our study is the Bargmann transform which provides a coupling between the classical (real) and analytic…
The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $x{\rightarrow}\bar{x}^{\bar{\alpha}}$ has long been used as a method of simplifying spectral problems in quantum mechanics. This…
In this work we take a closer look at the algebraic-operator correspondence between the momentum space and the position space which defines the form of the canonical momentum operator in position space in Quantum Mechanics (QM). Starting…
Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment…
To describe charged particles interacting with the quantized electromagnetic field, we point out the differences of working in the so-called generalized and the true Coulomb gauges. We find an explicit gauge transformation between them for…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…
We survey the operator algebras arising as commutants modulo normed ideals of finite sets of hermitian operators and connections to perturbations of operators and noncommutative geometry.
We investigate the kernels of the transformation operators for one-dimensional Schroedinger operators with potentials, which are asymptotically close to Bohr almost periodic infinite-gap potentials.
Starting from generalized position operators, we derive complex and quaternionic angular momentum operators along with their commutation algebra as well. These algebras differ from the standard Hermitian ones, especially in terms of…
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young…
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…