Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty principle in quantum mechanics with Newton's gravity   A new derivation is given of the known generalized position-momentum
uncertainty relation, which takes into account gravity. The problem of two
massive particles, the relative motion of which is described by the
Schroedinger equation, is considered. The potential energy is defined as a sum
of `standard' non-gravitational term and the second one, which corresponds to
gravitational attraction of particles as in Newton's theory of gravity. The
Green's function method is applied to solve the Schroedinger equation. It is
assumed that the solution of the problem in the case, when the gravitational
interaction is turned off, is known. Gravity is taken into account in linear
approximation with respect to the gravitational coupling constant made
dimensionless. Dimensional coefficients at additional squares of mean-square
deviations of position and momentum are written explicitly. The minimum length,
determined as minimal admissible distance between two quantum particles, and
the minimum momentum appear to be depending on the energy of particles'
relative motion. The theory allows one to present the generalized
position-momentum uncertainty relation in a new compact form.

6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph