Related papers: Schrodinger-Newton wave mechanics. The model
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
Starting from first principles and general assumptions based on the energy-momentum relation of the Special Theory of Relativity we present a novel wave equation for ultrarelativistic matter. This wave equation arises when particles satisfy…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
With the simplest proof ever, we justify the significance of quantum-gravity in non-relativistic quantum mechanics together with the related theories and experiments. Since the de Broglie wave length is inverse proportional to the mass, it…
It has been suggested by Diosi and Penrose that the occurrence of quantum state reduction in macroscopic objects is related to a manifestation of gravitational effects in quantum mechanics. Although within Penrose's framework the dynamics…
We investigate a $D$ dimensional generalization of the Schroedinger-Newton equations, which purport to describe quantum state reduction as resulting from gravitational effects. For a single particle, the system is a combination of the…
The family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a…
We investigate the implication of the non-linear and non-local multi-particle Schroedinger-Newton equation for the motion of the mass centre of an extended multi-particle object, giving self-contained and comprehensible derivations. In…
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schr\"odinger equation is approximated…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
The main goal of this brief report is to provide some new insight into how promising the Schroedinger-Newton equation would be to explain the emergence of classicality. Based on the similarity of the Newton and Coulomb potentials, we add an…
We regard the real and imaginary parts of the Schrodinger wave function as canonical conjugate variables.With this pair of conjugate variables and some other 2n pairs, we construct a quadratic Hamiltonian density. We then show that the…
Recently, we have presented a local-ether wave equation incorporating a nature frequency and the electric scalar potential, from which the speed-dependences in the angular frequency and wavelength of matter wave, in the mass of particle,…
The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is with the…
This paper systematically develops the Schr\"odinger formalism that is valid also for gyrotropic media where the material weights $W = \left ( \begin{smallmatrix} \varepsilon & \chi \chi^* & \mu \end{smallmatrix} \right ) \neq \overline{W}$…
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling…
We solve the Schr\"odinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the…
We briefly review our works for graviton and spherical graviton potentials in a plane-wave matrix model. To compute them, it is necessary to devise a configuration of the graviton solutions, since the plane-wave matrix model includes mass…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…