Related papers: Quantum and semi-classical aspects of confined sys…
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the…
We study the canonical and the coherent state quantization of a particle moving in a magnetic field on a non-commutative plane. Starting from the so called \theta-modified action, we perform the canonical quantization and analyze the gauge…
We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
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. - This is motivated by the ``timeless''…
The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the…
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…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
Semiclassical approximations to quantum dynamics are almost as old as quantum mechanics itself. In the approach pioneered by Wigner, the evolution of his quasiprobability density function on phase space is expressed as an asymptotic series…
Classical mechanics is formulated in complex 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…
An inhomogeneous Kaluza-Klein compactification to four dimensions, followed by a conformal transformation, results in a system with position dependent mass (PDM). This origin of a PDM is quite different from the condensed matter one. A…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a…
Algebraic quantization scheme has been proposed as an extension of the Dirac quantization scheme for constrained systems. Semi-classical states for constrained systems is also an independent and important issue, particularly in the context…
It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there…
The trace of an arbitrary product of quantum operators with the density operator is rendered as a multiple phase space integral of the product of their Weyl symbols with the Wigner function. Interspersing the factors with various evolution…