Self-adjoint time operators and invariant subspaces

DOI10.1016/S0034-4877(08)80004-3zbMath1155.47010arXivmath-ph/0607041OpenAlexW2061732944MaRDI QIDQ931887

Fernando Palacios Gómez

Publication date: 3 July 2008

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0607041

zbMATH Keywords

invariant subspaceinnovationcanonical commutation relationtime operatorWeyl commutation relationAharonov-Bohm time operatorintrinsic randomnessLax-Phillips scatteringSchrödinger couple

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Invariant subspaces of linear operators (47A15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Dilations, extensions, compressions of linear operators (47A20) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Canonical models for contractions and nonselfadjoint linear operators (47A45)

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Cites Work

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• Lax--Phillips evolutions in quantum mechanics and two-space scattering.
• Time operators for one parameter semigroups
• Characterizations of intrinsically random dynamical systems
• Translation invariant spaces
• Classification of certain pairs of operators (P,Q) satisfying \([P,Q=- iId\)]
• Dilations of symmetric operators shifted by a unitary group
• The time operator of wavelets
• On intrinsic randomness of dynamical systems
• On necessary and sufficient conditions for the existence of time and entropy operators in quantum mechanics
• Relativistic internal time operator
• Dirac kets, Gamov vectors and Gel'fand triplets. The rigged Hilbert space formulation of quantum mechanics. Lectures in mathematical physics at the University of Texas at Austin, USA. Ed. by A. Bohm and J. D. Dollard
• Canonical commutation relations of quantum mechanics and stochastic regularity
• The nondemolition measurement of quantum time
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• Time operators, innovations and approximations.
• Die Eindeutigkeit der Schrödingerschen Operatoren
• Time operator for diffusion.
• On the Heisenberg commutation relation. I
• The time operator of the cusp map
• Doubly invariant subspaces
• On two problems concerning linear transformations in Hilbert space
• A generalized Weyl relation approach to the time operator and its connection to the survival probability
• Time in the Quantum Theory and the Uncertainty Relation for Time and Energy
• Shifts on Hilbert spaces.
• Non-unitary transformation of conservative to dissipative evolutions
• From deterministic dynamics to probabilistic descriptions
• Time in Quantum Mechanics
• Pauli's theorem and quantum canonical pairs: the consistency of a bounded, self–adjoint time operator canonically conjugate to a Hamiltonian with non–empty point spectrum
• TIME OPERATOR IN QUANTUM MECHANICS AND SOME STOCHASTIC PROCESSES WITH LONG MEMORY
• Simply invariant subspaces