We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the term of the second order. To escape technical difficulties related to the infinite dimension of phase space f...

This chapter gives a brief introduction to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take...

Recent years have witnessed a great research boom in soft matter physics. By now, most advances, however, are of empirical results or purely mathematical extensions. The major obstacle is lacking of insights into fundamental physical laws underlying fractal mesostructures of soft matter. This study will use fractional mathematics, which consists of fractal, fractional calculus, fractional Brown...

We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is avai...

Cλ-extended oscillator algebras, where Cλ is the cyclic group of order λ, are introduced and realized as generalized deformed oscillator algebras. For λ = 2, they reduce to the well-known Calogero–Vasiliev algebra. For higher λ values, they are shown to provide in their bosonic Fock space representation some interesting applications to supersymmetric quantum mechanics and some variants thereof:...

We present a review of the current state of affairs in the foundations of quantum meachanics. After introducing the axioms of quantum theory, the first part of the report examines in detail the trials of interpreting quantum mechanics in a realist way. The main focus of the second half of the review is the attempt to describe quantum mechanics within a larger space of hypothetical theories. A p...

Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme in terms of algebraic quantum theory.

Classical mechanics is formulated in Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of sem...

We demonstrate that reciprocal Maupertuis’ Principle is the classical limit of Schrödinger’s Variational Principle in Quantum Mechanics. Misha Marinov loved analytical mechanics and understood its beauty. Canonical transformations, Poisson structures, symplectic geometry etc. were the notions that he constantly used in his original papers, and in his famous review on path integral. One of the a...