Annals of physics, ISSN 0003-4916, 2008, Volume 323, Issue 2, pp. 500 - 526

We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480–494...

Similarity transform and Weyl ordering covariance | Weyl ordering | Weyl ordered Wigner operator | Entangled state representation | Wigner transform | The integration for ket–bra operators | The IWWOP technique | The integration for ket-bra operators | the integration for ket-bra operators | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL FOURIER-TRANSFORM | WIGNER-DISTRIBUTION | MODE | the IWWOP technique | entangled state representation | VIRTUE | IWOP TECHNIQUE | SQUEEZED STATES | similarity transform and Weyl ordering covariance | OPTICS | COHERENT-STATE REPRESENTATION | SYMPLECTIC TRANSFORMATIONS | Integrated approach | Mathematics | Statistical analysis | Physics | Quantum theory | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS | SIGNALS | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | TRANSFORMATIONS

Similarity transform and Weyl ordering covariance | Weyl ordering | Weyl ordered Wigner operator | Entangled state representation | Wigner transform | The integration for ket–bra operators | The IWWOP technique | The integration for ket-bra operators | the integration for ket-bra operators | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL FOURIER-TRANSFORM | WIGNER-DISTRIBUTION | MODE | the IWWOP technique | entangled state representation | VIRTUE | IWOP TECHNIQUE | SQUEEZED STATES | similarity transform and Weyl ordering covariance | OPTICS | COHERENT-STATE REPRESENTATION | SYMPLECTIC TRANSFORMATIONS | Integrated approach | Mathematics | Statistical analysis | Physics | Quantum theory | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS | SIGNALS | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | TRANSFORMATIONS

Journal Article

Chinese Physics B, ISSN 1674-1056, 05/2010, Volume 19, Issue 5, pp. 050303 - 0503037

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators...

S-ordered operator expansion formula | Technique of integration within s-ordered product of operators | S-parameterized generalized Wigner operator | S-parameterized quantization scheme | s-parameterized generalized Wigner operator | s-ordered operator expansion formula | s-parameterized quantization scheme | PHYSICS, MULTIDISCIPLINARY | technique of integration within s-ordered product of operators | COHERENT | NEWTON-LEIBNIZ INTEGRATION | KET-BRA OPERATORS | QUANTUM-MECHANICS | Quantization | Operators | Density | Quantum mechanics | Physics - Quantum Physics

S-ordered operator expansion formula | Technique of integration within s-ordered product of operators | S-parameterized generalized Wigner operator | S-parameterized quantization scheme | s-parameterized generalized Wigner operator | s-ordered operator expansion formula | s-parameterized quantization scheme | PHYSICS, MULTIDISCIPLINARY | technique of integration within s-ordered product of operators | COHERENT | NEWTON-LEIBNIZ INTEGRATION | KET-BRA OPERATORS | QUANTUM-MECHANICS | Quantization | Operators | Density | Quantum mechanics | Physics - Quantum Physics

Journal Article

Journal of Modern Optics, ISSN 0950-0340, 05/2013, Volume 60, Issue 9, pp. 769 - 771

The operator associated with the radially integrated Wigner function is found to lack justification as a phase operator.

quantum phase | Wigner function | Pegg-Barnett phase formalism | OPTICS | Physics - Quantum Physics

quantum phase | Wigner function | Pegg-Barnett phase formalism | OPTICS | Physics - Quantum Physics

Journal Article

PHYSICA SCRIPTA, ISSN 0031-8949, 12/2019, Volume 94, Issue 12, p. 124001

We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner-Weyl position-momentum phase-space, but another space...

Wigner Weyl | displacement operator completeness orthogonality | radar Ambiguity function | phase space quantum mechanics | PHYSICS, MULTIDISCIPLINARY | WIGNER

Wigner Weyl | displacement operator completeness orthogonality | radar Ambiguity function | phase space quantum mechanics | PHYSICS, MULTIDISCIPLINARY | WIGNER

Journal Article

International Journal of Applied Mathematics and Computer Science, ISSN 1641-876X, 09/2019, Volume 29, Issue 3, pp. 439 - 451

.... We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method...

spectral split-operator method | Moyal dynamics | Wigner distribution function | MATHEMATICS, APPLIED | MECHANICS | WIGNER FUNCTION | SCHRODINGER-EQUATION | REPRESENTATION | QUANTIZATION | DEFORMATION-THEORY | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Potential energy | Evolution | Algorithms | Equations of motion | wigner distribution function | moyal dynamics

spectral split-operator method | Moyal dynamics | Wigner distribution function | MATHEMATICS, APPLIED | MECHANICS | WIGNER FUNCTION | SCHRODINGER-EQUATION | REPRESENTATION | QUANTIZATION | DEFORMATION-THEORY | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Potential energy | Evolution | Algorithms | Equations of motion | wigner distribution function | moyal dynamics

Journal Article

Annals of Physics, ISSN 0003-4916, 2008, Volume 323, Issue 6, pp. 1502 - 1528

We show that Newton–Leibniz integration over Dirac’s ket-bra projection operators with continuum variables, which can be performed by the technique of integration within ordered product (IWOP) of operators...

Generalized Wigner operator | Bivariate-normal-distribution for normally ordered operators | Entangled Husimi operator | Entangled state representation | Integration for ket-bra operators | The IWOP technique | STATES | the IWOP technique | bivariate-normal-distribution for normally ordered operators | PHYSICS, MULTIDISCIPLINARY | MOMENTUM | LIGHT | COHERENT | entangled state representation | integration for ket-bra operators | generalized Wigner operator | IWOP TECHNIQUE | OPTICS | entangled Husimi operator | Normal distribution | Quantum physics | PHASE SPACE | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS

Generalized Wigner operator | Bivariate-normal-distribution for normally ordered operators | Entangled Husimi operator | Entangled state representation | Integration for ket-bra operators | The IWOP technique | STATES | the IWOP technique | bivariate-normal-distribution for normally ordered operators | PHYSICS, MULTIDISCIPLINARY | MOMENTUM | LIGHT | COHERENT | entangled state representation | integration for ket-bra operators | generalized Wigner operator | IWOP TECHNIQUE | OPTICS | entangled Husimi operator | Normal distribution | Quantum physics | PHASE SPACE | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS

Journal Article

Annals of physics, ISSN 0003-4916, 2006, Volume 321, Issue 2, pp. 480 - 494

Newton–Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., | q〉〈 q...

Radon transform | Wigner operator | The bipartitie entangled state | The IWOP technique | Squeezing operator | SQUEEZED STATES | PHASE | the IWOP technique | squeezing operator | PHYSICS, MULTIDISCIPLINARY | radon transform | LIGHT | the bipartitie entangled state | Atmospheric radon | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | QUANTUM OPERATORS | CLASSICAL MECHANICS | QUANTUM ENTANGLEMENT | FUNCTIONS | QUANTUM MECHANICS | TRANSFORMATIONS

Radon transform | Wigner operator | The bipartitie entangled state | The IWOP technique | Squeezing operator | SQUEEZED STATES | PHASE | the IWOP technique | squeezing operator | PHYSICS, MULTIDISCIPLINARY | radon transform | LIGHT | the bipartitie entangled state | Atmospheric radon | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | QUANTUM OPERATORS | CLASSICAL MECHANICS | QUANTUM ENTANGLEMENT | FUNCTIONS | QUANTUM MECHANICS | TRANSFORMATIONS

Journal Article

2017, Advanced textbooks in mathematics, ISBN 9781786343093, xx, 229 pages

Book

Modern physics letters. B, Condensed matter physics, statistical physics, applied physics, ISSN 1793-6640, 2019, Volume 33, Issue 26, p. 1950320

An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator [Formula: see text...

QUANTUM INFORMATION | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | Wigner function | nonclassicality | Orthogonalization | coherent state | PHYSICS, MATHEMATICAL | non-Gaussianity

QUANTUM INFORMATION | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | Wigner function | nonclassicality | Orthogonalization | coherent state | PHYSICS, MATHEMATICAL | non-Gaussianity

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 10/2019, Volume 33, Issue 28, p. 1950340

A simplified operator correspondence scheme is derived to address nonlinear quantum systems within the framework of the P -representation...

Nonlinear quantum optics | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | OPTICAL BISTABILITY | WIGNER FUNCTION | operator correspondence | MODEL | matter waves | PHYSICS, MATHEMATICAL | P-representation | OSCILLATOR

Nonlinear quantum optics | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | OPTICAL BISTABILITY | WIGNER FUNCTION | operator correspondence | MODEL | matter waves | PHYSICS, MATHEMATICAL | P-representation | OSCILLATOR

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2003, Volume 205, Issue 1, pp. 107 - 131

We study a class of pseudodifferential operators known as time–frequency localization operators, Anti-Wick operators, Gabor...

Feichtinger's algebra | Localization operator | Weyl calculus | Convolution relations | Wigner distribution | Modulation space | Short-time Fourier transform | Schatten class | localization operator | modulation space | convolution relations | DISTRIBUTIONS | AMALGAMS | MATHEMATICS | DECOMPOSITIONS | UNCERTAINTY PRINCIPLE | FOURIER-TRANSFORM | short-time Fourier transform | MODULATION SPACES

Feichtinger's algebra | Localization operator | Weyl calculus | Convolution relations | Wigner distribution | Modulation space | Short-time Fourier transform | Schatten class | localization operator | modulation space | convolution relations | DISTRIBUTIONS | AMALGAMS | MATHEMATICS | DECOMPOSITIONS | UNCERTAINTY PRINCIPLE | FOURIER-TRANSFORM | short-time Fourier transform | MODULATION SPACES

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 3/2016, Volume 55, Issue 3, pp. 1741 - 1752

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite S n (λ...

Wigner function | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics, general | Multipartite entangled state | Physics | Elementary Particles, Quantum Field Theory | Squeezing operator | PHYSICS, MULTIDISCIPLINARY | CONTINUOUS-VARIABLES | ENTANGLED STATE | QUANTUM TELEPORTATION | GENERATION | Algebra

Wigner function | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics, general | Multipartite entangled state | Physics | Elementary Particles, Quantum Field Theory | Squeezing operator | PHYSICS, MULTIDISCIPLINARY | CONTINUOUS-VARIABLES | ENTANGLED STATE | QUANTUM TELEPORTATION | GENERATION | Algebra

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 1, pp. 304 - 318

...-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then considered...

Pseudo-differential operators | Time-frequency representations | Uncertainty principles | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY PROPERTIES | WIGNER DISTRIBUTIONS | MODULATION SPACES | PSEUDODIFFERENTIAL CALCULUS | TRANSFORMS

Pseudo-differential operators | Time-frequency representations | Uncertainty principles | MATHEMATICS | MATHEMATICS, APPLIED | CONTINUITY PROPERTIES | WIGNER DISTRIBUTIONS | MODULATION SPACES | PSEUDODIFFERENTIAL CALCULUS | TRANSFORMS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2017, Volume 446, Issue 1, pp. 920 - 944

We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform...

Linear partial differential operators with polynomial coefficients | Regularity | Schwartz spaces | Wigner transform | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs

Linear partial differential operators with polynomial coefficients | Regularity | Schwartz spaces | Wigner transform | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs

Journal Article

Physica Scripta, ISSN 0031-8949, 07/2015, Volume 90, Issue 7, pp. 1 - 8

A new integral representation is obtained for the star product corresponding to the s-ordering of the creation and annihilation operators...

Weyl-Wigner correspondence | Wick and anti-Wick symbols | Star product algebras | Deformation quantization | PHYSICS, MULTIDISCIPLINARY | star product algebras | deformation quantization | Kernels | Operators | Integrals | Mathematical analysis | Stars | Derivation | Representations | Order disorder

Weyl-Wigner correspondence | Wick and anti-Wick symbols | Star product algebras | Deformation quantization | PHYSICS, MULTIDISCIPLINARY | star product algebras | deformation quantization | Kernels | Operators | Integrals | Mathematical analysis | Stars | Derivation | Representations | Order disorder

Journal Article

JOURNAL OF SPECTRAL THEORY, ISSN 1664-039X, 2019, Volume 9, Issue 4, pp. 1287 - 1325

.... We prove that the partial trace of the full Hamiltonian converges, in resolvent sense, to an effective Schrodinger operator with magnetic field and a corrective electric potential that depends...

MATHEMATICS, APPLIED | WIGNER MEASURES | APPROXIMATION | Pauli-Fierz model | magnetic Schrodinger operators | POTENTIALS | SELF-ADJOINTNESS | MATHEMATICS | PHASE | magnetic Laplacians | Quasi-classical limit | DYNAMICS | CONVERGENCE

MATHEMATICS, APPLIED | WIGNER MEASURES | APPROXIMATION | Pauli-Fierz model | magnetic Schrodinger operators | POTENTIALS | SELF-ADJOINTNESS | MATHEMATICS | PHASE | magnetic Laplacians | Quasi-classical limit | DYNAMICS | CONVERGENCE

Journal Article

中国科学：物理学、力学、天文学英文版, ISSN 1674-7348, 2012, Volume 55, Issue 5, pp. 762 - 766

In quantum mechanics theory one of the basic operator orderings is Q - P and P - Q ordering, where Q and P are the coordinate operator and the momentum operator, respectively...

坐标算符 | 量子力学理论 | 动量算符 | 公式推导 | 订货 | 操作顺序 | 运营商 | 集成技术 | operator-ordering identities | Wigner operator | mathfrak{Q} | ordering | mathfrak{P} | ordering and | IWOP technique | Physics, general | Physics | Classical Continuum Physics | Astronomy, Observations and Techniques | Operator-ordering identities | Q-ordering and P-ordering | PHASE-SPACE | INTEGRATION | PHYSICS, MULTIDISCIPLINARY

坐标算符 | 量子力学理论 | 动量算符 | 公式推导 | 订货 | 操作顺序 | 运营商 | 集成技术 | operator-ordering identities | Wigner operator | mathfrak{Q} | ordering | mathfrak{P} | ordering and | IWOP technique | Physics, general | Physics | Classical Continuum Physics | Astronomy, Observations and Techniques | Operator-ordering identities | Q-ordering and P-ordering | PHASE-SPACE | INTEGRATION | PHYSICS, MULTIDISCIPLINARY

Journal Article

Journal of the Optical Society of America A: Optics and Image Science, and Vision, ISSN 1084-7529, 10/2013, Volume 30, Issue 10, pp. 2096 - 2100

.... In this paper, we find a linear, second-order, self-adjoint differential commuting operator that commutes with the LCT operator...

OPTICAL-SYSTEMS | HARMONIC-OSCILLATOR | INVERTED OSCILLATOR | FRACTIONAL FOURIER-TRANSFORM | WIGNER DISTRIBUTION | OPTICS | QUANTUM-MECHANICS | Operators | Mathematical analysis | Transforms | Exact solutions | Differential equations | Eigenvalues | Eigenfunctions | Cylinders

OPTICAL-SYSTEMS | HARMONIC-OSCILLATOR | INVERTED OSCILLATOR | FRACTIONAL FOURIER-TRANSFORM | WIGNER DISTRIBUTION | OPTICS | QUANTUM-MECHANICS | Operators | Mathematical analysis | Transforms | Exact solutions | Differential equations | Eigenvalues | Eigenfunctions | Cylinders

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 474, Issue 2, pp. 1238 - 1249

Let H be a complex Hilbert space whose dimension is not less than 3 and let Fs(H) be the real vector space formed by all self-adjoint operators of finite rank on H...

Wigner's type theorems | Projection | Hilbert Grassmannian | Self-adjoint operator of finite rank | MATHEMATICS | MATHEMATICS, APPLIED | SET | N-DIMENSIONAL SUBSPACES | TRANSFORMATIONS

Wigner's type theorems | Projection | Hilbert Grassmannian | Self-adjoint operator of finite rank | MATHEMATICS | MATHEMATICS, APPLIED | SET | N-DIMENSIONAL SUBSPACES | TRANSFORMATIONS

Journal Article

DOCUMENTA MATHEMATICA, ISSN 1431-0643, 2017, Volume 22, pp. 727 - 776

Making use of the localised Putnam theory developed in [GJ1], we show the limiting absorption principle for Schrodinger operators with perturbed oscillating potential on appropriate energy intervals...

MATHEMATICS | NEUMANN-WIGNER POTENTIALS | PERTURBATIONS | LOWER BOUNDS | INEQUALITY | SYSTEMS | ABSENCE | MOURRES COMMUTATOR THEORY | SCATTERING-THEORY | CONTINUOUS-SPECTRUM | POSITIVE EIGENVALUES

MATHEMATICS | NEUMANN-WIGNER POTENTIALS | PERTURBATIONS | LOWER BOUNDS | INEQUALITY | SYSTEMS | ABSENCE | MOURRES COMMUTATOR THEORY | SCATTERING-THEORY | CONTINUOUS-SPECTRUM | POSITIVE EIGENVALUES

Journal Article

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