Geometric dynamics of a harmonic oscillator, arbitrary minimal uncertainty states and the smallest step 3 nilpotent Lie group

DOI10.1088/1751-8121/aaed4dzbMath1422.81124arXiv1805.01399OpenAlexW2885996762WikidataQ61821518 ScholiaQ61821518MaRDI QIDQ5235188

Fadhel Almalki, G.V.P.Khmelevskaya

Publication date: 7 October 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01399

zbMATH Keywords

coherent statesharmonic oscillatorsqueezed states

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Schrödinger operator, Schrödinger equation (35J10) Coherent states (81R30) General properties and structure of real Lie groups (22E15) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (9)

Solving the Schrödinger equation by reduction to a first-order differential operator through a coherent states transform ⋮ Quantizations on the Engel and the Cartan groups ⋮ New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis ⋮ Tuning co- and contra-variant transforms: the Heisenberg group illustration ⋮ Metamorphism -- an integral transform reducing the order of a differential equation ⋮ Metamorphism as a covariant transform for the SSR group ⋮ Cross-Toeplitz operators on the Fock-Segal-Bargmann spaces and two-sided convolutions on the Heisenberg group ⋮ An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library ⋮ A note on spectral multipliers on Engel and Cartan groups

Cites Work

• Unnamed Item
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• Quantum blobs
• Induced representations and hypercomplex numbers
• Coherent states, wavelets, and their generalizations
• Hypercomplex representations of the Heisenberg group and mechanics
• Banach spaces related to integrable group representations and their atomic decompositions. I
• Lectures on Gaussian integral operators and classical groups
• Shearlets. Multiscale analysis for multivariate data.
• Banach spaces related to integrable group representations and their atomic decompositions. II
• \({\mathcal D}\)-pseudo-bosons, complex Hermite polynomials, and integral quantization
• Quantum mechanics and nilpotent groups. I: The curved magnetic field
• Higher-order polarizations on the Virasoro group and anomalies
• Maxwell strata and cut locus in the sub-Riemannian problem on the Engel group
• Wavelets in Banach spaces
• Symplectic geometry and quantum mechanics
• The representations of the oscillator group
• Operator covariant transform and local principle
• Induced Representations of Locally Compact Groups
• Uncertainty and Analyticity
• Coherent States from Nonunitary Representations
• The quantum Arnold transformation
• Analytic representations in quantum mechanics
• Symplectic Methods in Harmonic Analysis and in Mathematical Physics
• Harmonic Analysis in Phase Space. (AM-122)
• Canonical transforms, separation of variables, and similarity solutions for a class of parabolic differential equations
• The quartic anharmonic oscillator and its associated nonconstant magnetic field
• p-mechanics as a physical theory: an introduction
• On the Quantum Mechanics of Squeezed States
• Symmetry, Geometry and Quantization with Hypercomplex Numbers
• Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0
• Wavelets beyond admissibility
• Non-Hermitian Coherent States for Finite-Dimensional Systems
• An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library
• ABC of ladder operators for rationally extended quantum harmonic oscillator systems
• Squeezed states and Hermite polynomials in a complex variable
• Quantum Optics
• Boundedness for Pseudo-differential Calculus on Nilpotent Lie Groups
• Possible Kinematics
• Induced Representations of Locally Compact Groups and Applications
• Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes
• Lie group representations and quantization

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