ﻻ يوجد ملخص باللغة العربية
In this work we consider an extraordinary quantum mechanical effect when, roughly speaking, the nucleus of an atom becomes (linearly) larger than the whole atom. Precisely, we consider Helium ion (in the ground state of the electron) moving translationally with the speed much smaller than speed of the electron rotation. This translation, effectively, changes neither the total momentum, nor the de Broglie wave length of the electron, nor the linear size of the atom corresponding to the diameter of the electron orbit. But, this translation implies a small nucleus momentum and nuclear de Broglie wavelength almost hundred times larger than the electron de Broglie wavelength. In the measurement of the nucleus wavelength using a diffraction apparatus with a characteristic length constant proportional to the proposed nucleus wavelength, according to standard quantum mechanical formalism, the nucleus behaves practically certainly as a wave. Then the unique, irreducible linear characteristic size for such a nucleus is de Broglie wavelength. Such a measurement effectively influences neither the electron dynamics nor linear size of the atom. This implies that, in such measurement, the size of the nucleus is in one dimension larger than the whole atom, i.e. electron orbital. All this corresponds metaphorically to the famous Leonardo fresco Last Supper where Jesus words coming from the nucleus, i.e. center of the composition, cause an expanding superposition or dramatic wave-like movement of the apostles.
I show that Matsumoto conjectured inequality between relative length and Finsler length is false. The incorrectness of the claim is easily inferred from the geometry of the indicatrix.
General Relativity has had tremendous successes on both theoretical and experimental fronts for over a century by now. However, the theory contents are far from being exhausted. Only very recently, with gravitational wave detection from colliding bla
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to generalize th
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. By this definition, turbulence always cascades from small scales where vorti