相关论文: Symplectic Structures and Quantum Mechanics

Canonical coordinates for both the Schroedinger and the nonlinear Schroedinger equations are introduced, making more transparent their Hamiltonian structures. It is shown that the Schroedinger equation, considered as a classical field…

The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…

Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…

In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…

This is the first in a two-part series in which we extend non-relativistic stochastic mechanics, in the ZSM formulation [1, 2], to semiclassical Newtonian gravity (ZSM-Newton) and semiclassical Newtonian electrodynamics (ZSM-Coulomb), under…

A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schr\"odinger equation has been launched. The introduced space-time fractional Schr\"odinger equation has a new scale…

A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a…

The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…

We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…

Going back to the early days in the history of quantum mechanics, the interaction of quantum and classical systems stands among the most intriguing open questions in science and makes its appearance in several fields, from physics to…

Path integral representations for generalized Schr\"odinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with L\'evy subordinators is used,…

A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…

We consider the spectral problem for the two-dimensional Schr\"odinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the…

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which…

The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…

This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…

This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…

Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…

An universal form of kinetic equation for open systems is considered which naturally unifies classical and quantum cases and allows to extend concept of wave function to open quantum systems. Corresponding stochastic Schr\"{o}dinger…