Related papers: On the dual structure of the Schr\"{o}dinger dynam…
We analyze the Schr\"{o}dinger dynamics and the Schr\"{o}dinger function (or the so-called wavefunction) in the following four aspects. (1) The Schr\"{o}dinger equation is reconstructed from scratch in the real field only, without referring…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential.…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
Recent developments in quantum physics make heavy use of so-called "quantum trajectories." Mathematically, this theory gives rise to "stochastic Schr\"odinger equations", that is, perturbation of Schr\"odinger-type equations under the form…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
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…
In non-relativistic quantum mechanics, path integrals are normally derived from the Schroedinger equation. This assumes the two formalisms are equivalent. Since time plays a very different role in the Schroedinger equation and in path…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
We show that the Schr\"odinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic…
A number of non-Markovian stochastic Schr\"odinger equations, ranging from the numerically exact hierarchical form towards a series of perturbative expressions sequentially presented in an ascending degrees of approximations are revisited…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
We develop a Schr\"{o}dinger-picture formulation for a scalar quantum field driven by a Lorentz-invariant white-noise field. The quantum state of the system is described by a stochastic wave functional that evolves according to a stochastic…
Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
Recently two generalized nonlinear Schr\"{o}dinger equations have been proposed by Chavanis [Eur. Phys. J. Plus 132 (2017) 286] by applying Nottale's theory of scale relativity relying on a fractal space-time to describe dissipation in…
We provide the exact analytic solution of the stochastic Schr\"odinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of…
Schr\"odinger-type eigenvalue problems are ubiquitous in theoretical physics, with quantum-mechanical applications typically confined to cases for which the eigenfunctions are required to be normalizable on the real axis. However, seeking…
The stochastic Schr\"odinger equation, of classical or quantum type, allows to describe open quantum systems under measurement in continuous time. In this paper we review the link between these two descriptions and we study the properties…