相关论文: Canonical averaging of the equations of quantum me…

When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…

Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…

The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…

The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…

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…

Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…

The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics…

A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…

The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…

It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…

Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…

The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…

A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpreted as higher-order superintegrable perturbations of the 2D…

The time-dependent Schroedinger equation with time-independent Hamiltonian matrix is a homogeneous linear oscillatory system in canonical form. We investigate whether any classical system that itself is linear, homogeneous, oscillatory and…

We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by…