Related papers: Construction of quantum wavefunctions for non-sepa…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
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…
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem…
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
A gauge-invariant wave equation for the dynamics of hybrid quantum-classical systems is formulated by combining the variational setting of Lagrangian paths in continuum theories with Koopman wavefunctions in classical mechanics. We identify…
Using a nonlinear Schr\"{o}dinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
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…
We observe that, within the effective generating function formalism for the implementation of canonical transformations within wave mechanics, non-trivial canonical transformations which leave invariant the form of the Hamilton function of…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…