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Method for Construction of Unitary Operators in Quantum Field Theory

Paul H. Moravek, David W. Joseph

A method for the construction of explicit representations of unitary Hillbert-space operators in the particle-number representation is presented and illustrated by application to several examples.

Journal of Mathematical PhysicsNov 1, 19636 citations

Comment on “Arrival time in quantum mechanics” and “Time of arrival in quantum mechanics”

Jerzy Kijowski

Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

Physical Review AJan 1, 199945 citations

On the problem of recovering the ψ function in nonrelativistic quantum mechanics

Vladik Kreinovich

Theoretical and Mathematical PhysicsJul 1, 19768 citations

Self-adjoint Schrodinger and Dirac operators with Aharonov-Bohm and magnetic-solenoid fields

Dmitri M Gitman, Andrei Smirnov, Igor Viktorovich Tyutin +1 more

We study all the s.a. Schrodinger and Dirac operators (Hamiltonians) both with pure AB field and with magnetic-solenoid field. Then, we perform a complete spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulas. In constructing the Hamiltonians and performing their spectral analysis, we respectively follow the von Neumann theory of s.a. extensions of symmetric differential operators and the Krein method of guiding functionals. The examples of similar consideration are given by us in arXiv:0903.5277, where a nonrelativistic particle in the Calogero potential field is considered and in Theor. Math. Phys. 150 (1) (2007) 34, where a Dirac particle in the Coulomb field of arbitrary charge is considered. However, due to peculiarities of the three-dimensional problems under consideration, we elaborated a generalization of the approach used in the study of the Dirac particle.We study all the s.a. Schrodinger and Dirac operators (Hamiltonians) both with pure AB field and with magnetic-solenoid field. Then, we perform a complete spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulas. In constructing the Hamiltonians and performing their spectral analysis, we respectively follow the von Neumann theory of s.a. extensions of symmetric differential operators and the Krein method of guiding functionals. The examples of similar consideration are given by us in arXiv:0903.5277, where a nonrelativistic particle in the Calogero potential field is considered and in Theor. Math. Phys. 150 (1) (2007) 34, where a Dirac particle in the Coulomb field of arbitrary charge is considered. However, due to peculiarities of the three-dimensional problems under consideration, we elaborated a generalization of the approach used in the study of the Dirac particle.

arXiv:0911.0946Nov 4, 20098 citations

UNITARY OPERATORS IN QUANTUM THEORY

IMPERIAL COLLEGE PRESS eBooksSep 1, 19950 citations

On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics

Roman Gennadievich Novikov, Iskander Asanovich Taimanov

Annales Henri PoincaréFeb 5, 20246 citations

Explicit Construction of Unitary Operators in Nonrelativistic Quantum Mechanics

Abstract

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Explicit Construction of Unitary Operators in Nonrelativistic Quantum Mechanics

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