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We investigate operator algebraic origins of the classical Koopman-von Neumann wave function $\psi_{KvN}$ as well as the quantum mechanical one $\psi_{QM}$. We introduce a formalism of Operator Mechanics (OM) based on a noncommutative…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
When a quantum system interacts with an external environment, it undergoes the loss of quantum correlation (decoherence) and the loss of energy (relaxation) and eventually all of the quantum information becomes classical. Here we show a…
Quantum experiments detect particles, but they reveal information about wave properties. No matter how quanta are detected, they always express the local net state of the corresponding wave-function. The mechanism behind this process is…
The problem of the observer in quantum mechanics is getting new human content. The paradox of Wigner's friend and its extended versions have observers who not only observe quantum phenomena, but communicate, have memories and even…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
Most of the mathematical approaches for quantum Langevin equation are based on the non-commutativity of the random force operators. Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation…
The role of response operators is well established in quantum mechanics. We investigate their use for universal quantum machine learning models of response properties in molecules. After introducing a theoretical basis, we present and…
We prove that a usual differential operator is formally the limit of quantum differential operators. For this purpose, we introduce the notion of twisted differential operator of infinite level and prove that, formally, such an object is…
The widely considered assertion is that the unitarity of quantum mechanical evolution assures the preservation of information. It is even promoted in popular literature as an established fact. (Susskind, 2008) Yet, a simple chain of…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
A quaternionic version of Quantum Mechanics is constructed using the Schwinger's formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…