Related papers: Time in Quantum Mechanics
There are enough reasons for us to consider time as a dynamical variable or operator; but according to Pauli's argument the existence of a self-adjoint time operator is incompatible with the semi-boundedness of Hamiltonian spectrum. In this…
In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
W. Pauli pointed out that the existence of a self-adjoint time operator is incompatible with the semibounded character of the Hamiltonian spectrum. As a result, people have been arguing a lot about the time-energy uncertainty relation and…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
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.…
The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
The problem of time in quantum mechanics concerns the fact that in the Schr\"odinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The spacetime-position operator acts in the Hilbert space of functions of space…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
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…
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…
In the framework of any quantum theory in the Schroedinger picture a general operator time concept is given. For this purpose certain systems are emphasized as ideal quantum clocks. Their definition follows heuristically from a common…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…