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Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems,…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
The most general mathematical law for summing bounded quantities is not the arithmetic law, but a composition law of which the summation law for velocities in special relativity is only one particular example. We believe that this…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…
We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
We can recognize two modes in which 'quantum appears' in macro domains: (i) a 'micro-physical appearance', where quantum laws are assumed to be universal and they are transferred from the micro to the macro level if suitable 'quantum…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We critically revisit the issue of power-law running in models with extra dimensions. The general conclusion is that, in the absence of any additional physical principle, the power-corrections tend to depend strongly on the details of the…
Quantum Rings have been simulated so far in many ways, but in this work a new aproximation is deemed. We use particles without angular momentum and several spectra, for different geometric settings, are gotten. These spectra depends on K,…
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors…
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics.…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and…