Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized Weyl relation approach to the time operator and its
  connection to the survival probability   The time operator, an operator which satisfies the canonical commutation
relation with the Hamiltonian, is investigated, on the basis of a certain
algebraic relation for a pair of operators T and H, where T is symmetric and H
self-adjoint. This relation is equivalent to the Weyl relation, in the case of
self-adjoint T, and is satisfied by the Aharonov-Bohm time operator T_0 and the
free Hamiltonian H_0 for the one-dimensional free-particle system. In order to
see the qualitative properties of T_0, the operators T and H satisfying this
algebraic relation are examined. In particular, it is shown that the standard
deviation of T is directly connected to the survival probability, and H is
absolutely continuous. Hence, it is concluded that the existence of the
operator T implies the existence of scattering states. It is also shown that
the minimum uncertainty states do not exist. Other examples of these operators
T and H, than the one-dimensional free-particle system, are demonstrated.

5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph