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Quantum Theory of Galactic Dynamics Cosmological Mass Accumulations Described by s p d f g h i... Symmetry Quantised Gravity and Mass Spectra Within the Lambda Based Dust Universe Model

James G. Gilson
Year: 2012 Pages: 31
Keywords: Dust Universe, Dark Energy, Dark Matter, Newton's Gravitation Constant, Einstein's Cosmological Constant, Cosmological Mass Spectra, Quantised Gravity
Much of the introductory section of this paper is devoted to displaying some previously obtained formulae, incorporating a change of notation and variables and giving some explanation of the relation of the work to Newtonian gravitation theory. This section all refers to a quantisation of gravity concentrated on and limited to galaxies with totally spherically symmetric cores and halos. Only the radial variable r is involved and the emphasis is on the dark matter concept. All the following sections are devoted to generalising the theory to additionally incorporate a dependence of galactic structure on the theta and phi spherical angular coordinates. The theory is derived using Schroedinger quantum theory in much the same way as it was used in developing the theory of atomic structure. The theoretical structure to be developed in this papers is a hybrid formulation involving three fundamental theoretical facets, general relativity, Schroedinger quantum mechanics and a new theoretical version of isothermal gravity self equilibrium. The combined structure has only become possible because of the discovery of an infinite discrete set of equilibrium states associated with this later theory, the l parameter states. The configuration space structure of these states has been found to be available in Schr\"odinger theory from a special inverse square law potential which appears to supply an inverse cube self attraction to the origin that maintains galaxies in an isolated steady state self gravity quantum condition. The arbitrary numerical coefficients of these Schroedinger states can also depend on l and are appropriately imported from the isothermal equilibrium theory. The work discussed here is much about how these l states can be interleaved with with the usual Schroedinger parameter for angular momentun which I call l-prime to avoid confusion. The l values have been found to be two possible cases of infinite subsets of the l-prime values, a D set for the usual mass density distributions in galaxies and an P set for Einstein's extra pressure term density 3P/c^2. However these identifications are just a working hypothesis. The usual atomic electron theory approach of separation of variables is used to solve the general gravitational Schr\"odinger equation and it turns out to be rather simpler than the atomic electronic situation. Two version of adapting the Schr\"odinger equation to hold the isothermal l states are given. The first I call a transplant operation that in fact is a replacement of appropriate Schroedinger l-prime angular momentum state representations with isothermal l state representations. The second version is in the conclusions section and involves simply displaying restricted Schroedinger representations that describe various gravitational situations. Also in this section, it is made clear that each of the one component Schroedinger representations can be replaced with an equivalent two component representation consisting of a Laplace equation together with a quantised energy equation. Finally, I display the mapping of the angular symmetry defining letters from atomic theory into the quantum theory structure of the isothermal l states. The main products of the theory are a quantisation of the gravitational field with explicitly a refined collections of mass accumulation spectra and a generalisation of Newtonian gravitation theory based on general relativity.