相关论文: Ladder operators for isospectral oscillators

The q-difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.

Although there is no canonical version of the harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ so far, we make a strong case for a particular choice of operator by using the representation theory of the Dynin-Folland group…

We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator.…

The Heisenberg algebra is deformed with the set of parameters ${q, l,\lambda}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly…

The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a physical system in both elementary quantum mechanics and quantum field theory. This…

We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…

Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the…

Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…

Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to…

A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…

Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…

This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schr\"odinger equation for a free particle, the work derives…

Second degree polynomial Heisenberg algebras are realized through the harmonic oscillator Hamiltonian, together with two deformed ladder operators chosen as the third powers of the standard annihilation and creation operators. The…

We conjecture that the renormalized perturbative $S$-matrix of quantum field theory coincides with the evolution operator of the standard functional differential Schrodinger equation whose right hand side (quantum local Hamiltonian) is…

A comparison is made between bispectral operator pairs and dual pairs of isomonodromic deformation equations. Through examples, it is shown how operators belonging to rank one bispectral algebras may be viewed equivalently as defining…

We address the problem of phase shift operator acting as time evolution operator in Pegg-Barnett formalism. It is argued that standard shift operator is inconsistent with the behaviour of the state vector under cyclic evolution. We consider…

We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family of graph building operators $H_\alpha$ for ladder diagrams is constructed and investigated. The complete…

A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable $x$ and ${\d\over \d x}$ (the minimal canonical representation). The eigenstates of the Hamiltonian operator are found (at lower…