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We formulate a variational principle for non-relativistic quantum mechanics inspired by Gauss's principle of least constraint. We define a quantum constraint functional as the probability-weighted square deviation between the actual motion…
The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an…
A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Products and tensor products are linked by a universal property. Imposing the invariance of the laws of Nature under tensor composition along with Leibniz identity determines quantum and classical mechanics algebraic structure through the…