Related papers: How to Introduce Time Operator
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
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.…
Arguments are given that time must be defined in an operative manner,i.e., by constructing devices which can serve as clocks.The investigation of such devices leads to the conclusion that there is a principal uncertainity of time if one…
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…
Motivated by the parametrization invariance of cosmological Lagrangians and their equivalence to systems describing the motion of particles in curved backgrounds, we identify the phase space analogue of the notion of proper time. We define…
We present a generic way of thinking about time machines from the view of a far away observer. In this model the universe consists of three (or more) regions: One containing the entrance of the time machine, another the exit and the…
We define the action operator in the consistent histories formalism, as the quantum analogue of the classical action functional, for the simple harmonic oscillator case. The action operator is shown to be the generator of time…
Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the…
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
Relations between integrals of time-ordered product of operators, and their representation in terms of energy-ordered products are studied. Both can be decomposed into irreducible factors and these relations are discussed as well. The…
We enhance elementary quantum mechanics with three simple postulates that enable us to define time observable. We discuss shortly justification of the new postulates and illustrate the concept with the detailed analysis of a delta function…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the…
We investigate time operators in the context of quantum time crystals in ring systems. A generalized commutation relation called the generalized weak Weyl relation is used to derive a class of self-adjoint time operators for ring systems…
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that…
We demonstrate that the time operator that measures the time of arrival of a quantum particle into chosen state can be defined as a self-adjoint quantum-mechanical operator using periodic boundary conditions on applied to wavefuncions in…
The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of…
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…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
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…