相关论文: Quantization of the classical action and eigenvalu…
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…
There exists a paradigm in which Quantum Mechanics is an exclusively developed theory to explain phenomena on a microscopic scale. As the Planck's constant is extremely small, $h\sim10^{-34}{J.s}$, and as in the relation of de Broglie the…
In this paper we show that a method of quantization proposed few years ago (ann.of phys. (314),2005, 24) is equivalent to studying the system for values of the action close to zero. In this paper we also study the behaviour when the action…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
In the conventional formulation of quantum mechanics, the initial description is given only for the physical system under study. It factors out the state for the experimenter. We argue that such description is incomplete and can lead to…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
The underlying physics of quantum mechanics has been discussed for decades without an agreed resolution to many questions. The measurement problem, wave function collapse and entangled states are mired in complexity and the difficulty of…
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
A certain non-linear non-local substitution is shown to transform the action of the self-interacting quantum field to the free one. The functional integrals in both theories are equal to each other. However, the integrations are performed…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription 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…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…