Related papers: A self-adjoint arrival time operator inspired by m…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
In this paper, we study self-adjointness and spectrum of operators of the form $$H=\displaystyle -\frac{d^2}{dx^2}+Fx, F>0 \quad\text{on} \quad \mathcal{H}=L^{2}(-L,L).$$ $H$ is called Stark operator and describes a quantum particle in a…
There are self-adjoint operators which determine both spectral and semispectral measures. These measures have very different commutativity and covariance properties. This fact poses a serious question on the physical meaning of such a…
We propose a covariant algorithm for relativistic ideal measurements and for relativistic continuous measurements, its non-relativistic limit results the algorithm of the Event-Enhanced Quantum Theory. Therefore an additional intrinsic…
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta…
Using the orthodox Weyl -- Wigner -- Stratonovich -- Cohen (WWSC) quantization rule we construct a time -- of -- arrival operator for a free particle on the circle. It is shown that this operator is self -- adjoint but the careful analysis…
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a…
We discuss minisuperspace aspects a non empty Robertson-Walker universe containing scalar matter field. The requirement that the Wheeler-DeWitt (WDW) operator be self adjoint is a key ingredient in constructing the physical Hilbert space…
We are focused on the idea that observables in quantum physics are a bit more than just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference…
The properties of the time-of-arrival operator for free motion introduced by Aharonov and Bohm and of its self-adjoint variants are studied. The domains of applicability of the different approaches are clarified. It is shown that the…
We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the…
A suitable operator for the time-of-arrival at a detector is defined for the free relativistic particle in 3+1 dimensions. For each detector position, there exists a subspace of detected states in the Hilbert space of solutions to the Klein…
We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…
It has always been believed that no self-adjoint and canonical time of arrival operator can be constructed within the confines of standard quantum mechanics. In this Letter we demonstrate the otherwise. We do so by pointing out that there…
In this article, we review the general quantum mechanical setting associated to a non self-adjoint Hamiltonian with real spectrum. Spectral properties of the Hamiltonian of a simple model of the Swanson type are investigated. The…
Aim of this paper is 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 specifically,…
Considerable attention has been recently focused on quantum-mechanical systems with boundaries and/or singular potentials for which the construction of physical observables as self-adjoint (s.a.) operators is a nontrivial problem. We…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…