Related papers: Time in classical and quantum mechanics
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…
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…
In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
We replace the usual Hamiltonian constraint of quantum gravity H|psi>=0 by a weaker one <psi|H|psi>=0. This allows |psi> to satisfy the time-dependent functional Schrodinger equation. In general, only the phase of the wave function appears…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
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…
In the Schroedinger equation, time plays a special role as an external parameter. We show that in an enlarged system where the time variable denotes an additional degree of freedom, solutions of the Schroedinger equation give rise to…
The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental…
It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…
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…
Starting from our idea of combining the Feynman path integral spirit and the Dyson series kernel, we find an explicit and general form of time evolution operator that is a $c$-number function and a power series of perturbation including all…
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…
We introduce the notion of an extended moment in time, the duron. This is a region of temporal ambiguity which arises naturally in the nature of process which we take to be basic. We introduce an algebra of process and show how it is…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…