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In this article, we discard the bra-ket notation and its correlative definitions, given by Paul Dirac. The quantum states are only described by the wave functions. The fundamental concepts and definitions in quantum mechanics is simplified.…
By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
We reconstruct quantum mechanics by introducing "information operators" and excluding the concept of wave functions. Multiple information operators simultaneously describe a single system and continuously develop in time even in the process…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We propose a formulation of quantum mechanics in three dimensions with spherical symmetry for a finite level system whose dynamics is not governed by a differential equation of motion. The wavefunction is written as an infinite sum in a…
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 develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement…
The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account…
This is a non-technical presentation (in historical context) of the quantum theory that is strictly based on global unitarity. While the first part was written for a general readership, Sect. 5 may appear a bit provocative. I argue that the…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…
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…
The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to…