Connection between coherent states and some integrals and integral representations

• URL: http://arxiv.org/abs/2408.10749v1
• Date: Tue, 20 Aug 2024 11:31:15 GMT
• Title: Connection between coherent states and some integrals and integral representations
• Authors: Dušan Popov,
• Abstract summary: The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to calculate integrals or integral representations of different functions, expressible by means of Meijer's G-, as well as hypergeometric generalized functions.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to calculate integrals or integral representations of different functions, expressible by means of Meijer's G-, as well as hypergeometric generalized functions. The feedback starts from a fundamental integral that comes from the decomposition of the unity operator in the language of coherent states from quantum mechanics. In this way, integrals and integral representations are obtained, some that do not appear in the literature, and others already known, which can be verified by orthodox methods. All calculations are made using the properties of the diagonal operators ordering technique (DOOT), a relatively new technique of normal ordering of the creation and annihilation operators in quantum mechanics. The paper contributes to increasing the number of solvable integrals involving special functions.

Related papers

• Four-parameter Mittag-Leffler functions and their associated coherent states [0.0]
  The paper is an example of the application of a mathematical entity (Mittag-Leffler function) in quantum mechanics (coherent states formalism)
  arXiv  Detail & Related papers  (2024-10-25T10:46:21Z)
• Energy-filtered excited states and real-time dynamics served in a contour integral [0.0]
  The Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain. I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator.
  arXiv  Detail & Related papers  (2024-09-11T15:39:50Z)
• Quantum Rational Transformation Using Linear Combinations of Hamiltonian Simulations [0.0]
  We introduce effective implementations of rational transformations of a target operator on quantum hardware. We show that rational transformations can be performed efficiently with Hamiltonian simulations using a linear-combination-of-unitaries (LCU)
  arXiv  Detail & Related papers  (2024-08-14T18:00:01Z)
• An application of the theta operator in generalized hypergeometric coherent states formalism [0.0]
  We examine one of the multiple applications of theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs) A series of new results were obtained and some already known ones were found / confirmed. To support the theoretical considerations presented above, we examined, as example, the quantum systems with a linear energy spectrum.
  arXiv  Detail & Related papers  (2024-04-19T18:07:59Z)
• The tilted CHSH games: an operator algebraic classification [77.34726150561087]
  This article introduces a general systematic procedure for solving any binary-input binary-output game. We then illustrate on the prominent class of tilted CHSH games. We derive for those an entire characterisation on the region exhibiting some quantum advantage.
  arXiv  Detail & Related papers  (2023-02-16T18:33:59Z)
• Real quantum operations and state transformations [44.99833362998488]
  Resource theory of imaginarity provides a useful framework to understand the role of complex numbers. In the first part of this article, we study the properties of real'' (quantum) operations in single-party and bipartite settings. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations.
  arXiv  Detail & Related papers  (2022-10-28T01:08:16Z)
• Self-adjoint extension schemes and modern applications to quantum Hamiltonians [55.2480439325792]
  monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator theory and in applications to quantum mechanics. A number of models are discussed, which are receiving today new or renewed interest in mathematical physics, in particular from the point of view of realising certain operators of interests self-adjointly.
  arXiv  Detail & Related papers  (2022-01-25T09:45:16Z)
• Multicenter integrals involving complex Gaussian type functions [0.0]
  Multicentric integrals that involve a continuum state cannot be evaluated with the usual quantum chemistry tools. We show how such integrals can be evaluated analytically by using a representation of the continuum state by a set of complex Gaussian functions.
  arXiv  Detail & Related papers  (2021-11-16T16:58:55Z)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
  In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
  arXiv  Detail & Related papers  (2019-09-04T11:46:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.