Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: To know the quantum mechanical state of a particle implies restrictions
  on the results of measurements of its momentum   In the framework of the standard axioms of quantum mechanics, the wave
function of a particle in a one-dimensional configuration space (OCS)
determines not only the probability of its detection in the vicinity of the OCS
points, but also the local {\it average} values of the observables at these
points, which form the fields of the (operators) first initial moments of the
observables. The momentum operator field also determines the probability flow
rate in the OCS. Together with the field of the kinetic energy operator, it
defines {\it two} fields of particle momentum values. Their half-sum (the field
of local average values of the momentum) is determined in terms of the phase of
the wave function, and their half-difference (the deviation of the momentum
from the local average momentum) is determined in terms of its amplitude. The
average (over the ensemble) value of local momentum deviations at the OCS
points is equal to zero, and the average value of these deviations, multiplied
by the deviations of the coordinates of these points from the average (over the
ensemble) coordinate value, is equal to $\pm\hbar/2$.

27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg