Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relativistically Extended Modification of the Schroedinger Equation   We propose a nonlinear modification of the Schr\"{o}dinger equation that
possesses the main properties of this equation such as the Galilean invariance,
the weak separability of composite systems, and the homogeneity in the wave
function. The modification is derived from the relativistic relation between
the energy and momentum of free particle and, as such, it is the best
relativistic extension of the Schr\"{o}dinger equation that preserves the
properties in question. The only change it effectively entails in the
Schr\"{o}dinger equation involves the conserved probability current. It is
pointed out that it partially retains the linear superposition principle and
that it can be used to model the process of decoherence.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg