This is similar to the case of a nonrelativistic particle
The TFSE has been derived using the Feynman path integral technique for a nonrelativistic particle
. As expected the TFSE looks like a time fractional diffusion equation with an imaginary fractional diffusion constant but pertains to the realm of subdiffusion only, in contrast to Naber's generalization which includes superdiffusion as well.
The total energy loss of a nonrelativistic particle
passing through plasma may be quantized in units of h[[omega].sub.p], where [[omega].sub.p] is plasma frequency.
In this note, we demonstrated that the spectrum of the charged nonrelativistic particle
in the dense charged drop has a quantum structure (see (23)), and it is determined by three terms in the first mean field approximation.
Indeed if both the WIMP [chi] and the target with mass m are nonrelativistic particles
the cross section can be cast in the form
We imagined that the free electrons in metal as a gas of nonrelativistic particles
confined by the vacuum pressure in the interior of a cubic box of edge equal to d.
Neutrons with energies >20 MeV produce recoil protons and other heavy nonrelativistic particles
in a CsI(Tl) crystal, whereas gamma photons produce relativistic electrons.
We obtain that, for temperatures of order of the cosmic microwave radiation (i.e., T = 2.72 K), only photons and very light particles contribute to the energy radiation with [rho] ~ [10.sup.-51] [GeV.sup.4] and state equations, w = 1/3, whereas nonrelativistic particles
give negligible contributions .
This means that as the external fields become weak due to the increasing of the [alpha], the energy of the nonrelativistic particles
increases whereas the energy of the relativistic particles decreases.