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In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements, and modular variables, We present a physical explanation for the…
We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to $q$-versions of…
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the…
In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical…
We have performed an experimental test under the conditions of which quantum mechanics predicts a spatially-discontinuous single-particle transport. The transport is beyond the relativistic paradigm of movement in Cartesian space and…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the…
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
We propose a general construction of an observable measuring the time of occurence of an effect in quantum theory. Time delay in potential scattering is computed as a straightforward application.
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…