Authors: Guillermo A Rios
It's clear that by measuring the density profile ρ(r) of a dark matter galactic halo we are also indirectly measuring the mass of the dark matter particles (WIMPs.) So in this work we will derive such mass value mwimp from a current measured ρ(r) function. It's undeniable that gravitational fields affect the form and shape of the wave functions of quantum particles, and in the case of dark matter, where no other interaction is assumed acting, such gravitational fields are the only potential energy present in the Hamiltonian have an affect on the shape of the quantum wave function Ψwimp(r,t). Therefore to determine such wave function Ψwimp(r,t) of dark matter particles inside galactic halos, we will consider a quantum equation containing the gravitational potential energy due to the totality of the galactic matter, both baryonic and dark. At some point we will propose this, our derived quantum equation, as the sought after universal law for dark matter halos. Along all this process we will pay some special attention to the fact that we will be solving a quantum equation, including boundary conditions, etc, under very unusual circumstances in terms of lengths of galactic proportions, extremely large information travel time across the halo quantum system, etc. Finally, taking the Milky Way as our case of study, we will solve our equation to determine the mass mwimp of this elusive dark matter particle.
Comments: 41 Pages.
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