Related papers: A De Broglie-Like Wave in the Planetary Systems
We propose a new initial condition for the homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature.…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
In this note, we discuss a historical point regarding Schr\"odinger's discovery of the famous quantum wave equation in 1926 following de Broglie's fundamental works published in 1923-1925 regarding the introduction of matter waves. Drawing…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior.…
We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with…
It is shown that Schrodinger's equation and Born's rule are sufficient to ensure that the states of macroscopic collective coordinate subsystems are microscopically localized in phase space and that the localized state follows the classical…
Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order $m_{\rm…
In this paper I explain how I usually introduce the Schr\"odinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schr\"odinger equation belongs to a special case of wave equations I…
Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the `mostly empty' universe we observe around…
A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in…
A generalized true anomaly-type parametrization, convenient to describe both bound and open orbits of a two-body system in general relativity is introduced. A complete description of the time evolution of both the radial and of the angular…
The frequency of planets in binaries is an important issue in the field of extrasolar planet studies, because of its relevance in estimating of the global planet population of our Galaxy and the clues it can give to our understanding of…
We derive the tensor gravitational waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to second post-Newtonian order…
The Doppler shift of de Broglie wave is obtained for fermions and massive bosons using the conventional form of Lorentz transformations for momentum and energy of the particles. A formalism is developed to obtain the variation of wave…
We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…
We show that the de Broglie-Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade…
The significance of the de Broglie-Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the (orthodox) single-particle Newton-Wigner position. The effect of non-positive excursions of the ensemble…
In this work we suggest a simplified "quasi-classical" formalism of the Schwarzschild black hole thermodynamics. We define such small quantum system at Schwarzschild black hole horizon surface whose reduced Compton wavelength equals one…
In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have…