Related papers: What is Time in Quantum Mechanics?
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
We calculate the time of arrival probability distribution of a quantum particle using the Bohmian formalism. The pilot-wave is given by the wave function of the one dimensional vacuum squeezed state but written in the Schr\"odinger…
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…
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general…
We investigate a detector scheme designed to measure the arrival of a particle at $x=0$ during a finite time interval. The detector consists of a two state system which undergoes a transition from one state to the other when the particle…
It is shown that the time-dependent equations (Schr\"odinger and Dirac) for a quantum system can be always derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that…
We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in…
We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.
We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
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…
The paper consists of two parts. In the first part Schroedinger's equation for a charged quantum particle in a Galilei-Newton curved space-time is derived in a fully geometrical way. Gravitational and electromagnetic fields are coded into…
We compare the proposals that have appeared in the literature to describe a measurement of the time of arrival of a quantum particle at a detector. We show that there are multiple regimes where different proposals give inequivalent,…
General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…
We extend the concept of confined quantum time of arrival operators, first developed for the free particle [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)], to arbitrary potentials.
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…