Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty relations: curiosities and inconsistencies   Analyzing general uncertainty relations one can find that there can exist
such pairs of non-commuting observables $A$ and $B$ and such vectors that the
lower bound for the product of standard deviations $\Delta A$ and $\Delta B$
calculated for these vectors is zero: $\Delta A\,\cdot\,\Delta B \geq 0$. Here
we discuss examples of such cases and some other inconsistencies which can be
found performing a rigorous analysis of the uncertainty relations in some
special cases. As an illustration of such cases matrices $(2\times 2)$ and $(3
\times 3)$ and the position--momentum uncertainty relation for a quantum
particle in the box are considered. The status of the uncertainty relation in
$\cal PT$--symmetric quantum theory and the problems associated with it are
also studied.

37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph