Eigenvectors of two particles’ relative position and total momentum

From MaRDI portal
Publication:4286779

DOI10.1103/PhysRevA.49.704zbMath0979.47501OpenAlexW2039874890WikidataQ77875714 ScholiaQ77875714MaRDI QIDQ4286779

John R. Klauder, Hong-Yi Fan

Publication date: 11 April 1994

Published in: Physical Review A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1103/physreva.49.704




Related Items (83)

Measurement of quantum correlation on two-mode continuous stateEntanglement involved in time evolution of two-mode squeezed state in single-mode diffusion channelPhase-space representation of quantum state vectorsNewton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representationsHolomorphic Hermite polynomials in two variablesDeriving energy-gap of some Hamiltonians with kinetic coupling by the invariant eigen-operator methodEffective approach to constructing \(n\)-mode Wigner operator in the entangled state representationNew relation between input and output fields based on Collins diffraction formula and the Wigner function in entangled state representationSome unitary operators derived using the quantum state and its applicationEntangled state in quantization of magnetic flux qubits with mutual inductance couplingA kind of four-mode nonlinear entangled state representation in quantum opticsNew properties of the Wigner function of the tripartite entangled stateOperator realization of radial- and azimuthal- differentiations obtained by using the entangled state representationInfinitive operator-sum representation for damping in a squeezed heat reservoir via the thermo entangled state approachNew parameterized coherent-entangled state representation and its applicationsEntanglement swapping transform rule of entangled Wigner operatorsApplication of generalized EPR entangled state in quantum teleportationEntangled projector and a new approach for obtaining the entangled Wigner operator\(\mathfrak Q\)-, \(\mathfrak P\)-, and Weyl-ordering of squeezing operators: new operator identities and applicationsNew complex function space related to both entangled state representation and spin coherent stateEvolution of the number state in laser processState change, quantum probability, and information in operational phase-space measurementThe squeezing effect of three-mode operator as an extension from two-mode squeezing operatorQuantum Fresnel transformation responsible for squeezing mechanism and squeezed state of a degenerate parametric amplifierHankel transform as a transform between two entangled state representationsDevelopment in phase space quantum mechancis for constructing different masses' entangled state representationMultipartite State Representations in Multi-mode Fock Space and Their Squeezing TransformationsSolution to Operator Fredholm Equation in Bipartite Entangled State Representation and Its ApplicationsRepresentation of the coherent state for a beam splitter operator and its applicationsTemperature variation of chaotic optical field in quantum dissipation channel and diffusion channelSome quantum gate operators for continuum variables in \(q\)-deformed coordinate representationA new kind of bipartite coherent-entangled state and its applications in quantum opticsWeyl ordering of two-mode Fresnel operator and its applicationsSingle-mode photon-addition for the two-mode squeezed state and its statistical propertiesQuantum disentangling operator and squeezed vacuum state’s noise of a mesoscopic two-loop LC circuit with mutual inductanceA new kind of bipartite entangled state and some of its applicationsVirial theorem for angular displacement and torqueEntanglement rule of Wigner operators at a beamsplitterFour-mode coherent entangled state as an entanglement of two bipartite coherent entangled statesPath integral for the Hamiltonian of Josephson junctionStudying output states generated by optical beam splitter and 2-cascaded BSComplex wavelet transform of the Bell statesA new kind of representations on noncommutative phase spaceObtaining multimode entangled state representation by generalized Radon transformation of the Wigner operatorFresnel operator for deriving the propagator of 2D harmonic oscillator with cross couplingOn the \(s\)-parameterized quantization scheme for Dirac's representation theoryQuantum-mechanical Hankel transformation and ascending-lowering operators for the induced entangled state representationNew integration transformation connecting coherent state and entangled stateNew pair of mutually conjugate 3-mode entangled state representations and the corresponding fractional Fourier transformationEquivalence between SWH phase operator and Ban's phase operator revealed by virtue of \(|n\rangle\) representationEnergy level formula for the Morse oscillator with an additional kinetic coupling potentialA special type of squeezed coherent stateA convenient representation for the two-mode phase operator \(\sqrt{(\hat a+\hat b{}^\dag)/(\hat a{}^\dag+\hat b)}\)Number-difference-phase uncertainty relation for NFM operational quantum phase descriptionA kind of four-mode continuous-variable entangled state generated by beamsplitter and parametric down-conversionsNew two-mode canonical operator realization of angular momentum and generalized fractional Fourier transformation obtained via entangled state representationTime evolution and temperature variation of the squeezing-chaotic mixed two-mode optical field in one-mode diffusion channelEntangled state for constructing a generalized phase-space representation and its statistical behaviorPhase-space representation of quantum systems in the relative-state formulationDamping law of classical Weyl correspondence of density operator in amplitude dessipative channelFundamental entangling operators in quantum mechanics and their propertiesLaguerre-polynomial-weighted two-mode squeezed stateComplex wavelet transform of the two-mode quantum statesKraus operator-sum solution to the master equation describing the single-mode cavity driven by an oscillating external field in the heat reservoirDynamic evolution of squeezing maintenanceSpin coherent states as energy eigenstates of two coupled oscillators2N-mode squeezing operator gained by the entangled state representationA kind tripartite entangled state representation and its application in quantum teleportationEntangled Husimi distribution and complex wavelet transformationConvolution theorem for the three-dimensional entangled fractional Fourier transformation deduced from the tripartite entangled state representationGeneralized two-mode squeezed states and some nonclassical characteristicsQuantum dense coding with operational phase operator measurement studied by virtue of EPR eigenstate representationOptical Fresnel transform as a correspondence of the \(\text{SU}(1,1)\) squeezing operator composed of quadratic combination of canonical operators and the entangled stateDemonstration of Einstein-Podolsky-Rosen entanglement for an electron in a uniform magnetic fieldA novel 3D entangled wavelet transformation and its propertiesCoherence, Squeezing and Entanglement: An Example of Peaceful CoexistenceCommon eigenvectors of four particles' compatible observablesParametric amplifier studied as time evolution of angular momentum system in entangled state representationThe transformations from the new intermediate entangled stateReply to: Comment on `Equivalence between SWH phase operator and Ban's phase operator revealed by virtue of the \(|\eta\rangle\) representation'Classical Weyl correspondences of some two-mode quantum operators and their applicationApplication of entangled state representation to deriving normally ordered expansion of 1-dimensional Coulomb potentialGeneralized entangled Wigner operator for unifying three quantization schemes of entangled systems



Cites Work


This page was built for publication: Eigenvectors of two particles’ relative position and total momentum