Related papers: A selfadjoint variant of the time operator

A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to…

A large time expansion for the propagator associated to a semiclassical non-selfadjoint magnetic Schr\"odinger operator is established, in terms of the low lying eigenvalues of the operator.

Some results are reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory.…

Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More…

The problem of existence of a self-adjoint time operator conjugate to a Hamiltonian with SU(1,1) dynamical symmetry is investigated. In the space spanned by the eigenstates of the generator $K_3$ of the SU(1,1) group, the time operator for…

In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…

Although one can show formally that a time-of-arrival operator cannot exist, one can modify the low momentum behaviour of the operator slightly so that it is self-adjoint. We show that such a modification results in the difficulty that the…

Time operator is studied on the basis of field quantization, where the difficulty stemming from Pauli's theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative…

Algebraic and analytic aspects of self-adjoint operators of order four or more with polynomial coefficients are investigated. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain…

Time operator can be introduced by three different approaches: by pertaining it to dynamical variables; by quantizing the classical expression of time; taken as the restriction of energy shift generator to the Hilbert space of a physical…

This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.

Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics some properties of solutions of Schroedinger equation, related to Hilbert space formalism, are investigated for two types of time dependent…

For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the…

In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a…

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…

We study the properties of a quantum field with time as a dynamical variable. Temporal vibrations are introduced to restore the symmetry between time and space in a matter field. The system with vibrations of matter in time and space obeys…

A time operator is a Hermitian operator that is canonically conjugate to a given Hamiltonian. For a particle in 1-dimension, a Hamiltonian conjugate operator in position representation can be obtained by solving a hyperbolic second-order…

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation…

We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…