相关论文: On a Functional Equation of Ruijsenaars

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise…

Using Galois theory of functional equations, we give a new proof of the main result of the paper "Transcendental transcendency of certain functions of Poincar\'e" by J.F. Ritt, on the differential transcendence of the solutions of the…

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…

The Kronecker theta function is a quotient of the Jacobi theta functions, which is also a special case of Ramanujan's $_1\psi_1$ summation. Using the Kronecker theta function as building blocks, we prove a decomposition theorem for theta…

We consider the rational Heun operator defined as the most general second-order $q$-difference operator which sends any rational function of type $[(n-1)/n]$ to a rational function of type $[n/(n+1)]$. We shall take the poles to be located…

This paper reframes Riemannian geometry as a generalized Lie algebra allowing the equations of both RG and then General Relativity to be expressed as commutation relations among fundamental operators. We begin with an Abelian Lie algebra of…

In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anticommutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of…

A generalized quantum distribution function is introduced. The corresponding ordering rule for non-commuting operators is given in terms of a single parameter. The origin of this parameter is in the extended canonical transformations that…

We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the recurrence relations with…

Aichinger's equation is used to give simple proofs of several well-known characterizations of polynomial functions as solutions of certain functional equations. Concretely, we use that Aichinger's equation characterizes polynomial functions…

In this paper we present a simple method for deriving an alternative form of the functional equation for Riemann's Zeta function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work "Remarques…

We obtain a finite-sum representation for the general solution of the Jacobi second-order difference equation D(p(n-1)Du(n-1))+q(n)u(n)=l r(n)u(n) in terms of a nonvanishing solution corresponding to some fixed value of the spectral…

We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use…

We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…

Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…

A new representation of solutions to the equation $-y"+q(x)y=\omega^2 y$ is obtained. For every $x$ the solution is represented as a Neumann series of Bessel functions depending on the spectral parameter $\omega$. Due to the fact that the…

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the…

In this paper, a method to solve functionally commutative time- dependent linear homogeneous differential equation is discussed. We apply this technique to solve some dynamical quantum problems.

We prove a DuBois-Reymond necessary optimality condition and a Noether symmetry theorem to the recent quantum variational calculus of Cresson. The results are valid for problems of the calculus of variations with functionals defined on sets…

We conjecture the quantum analogue of the classical trace formulae for the integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This is done by departing from the classical construction where the corresponding model is…