Physics – Quantum Physics
Scientific paper
2000-06-19
Physics
Quantum Physics
16 pages, REVTeX. Accepted for publication in the Journal of Mathematical Physics
Scientific paper
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.
No associations
LandOfFree
A generalized Weyl relation approach to the time operator and its connection to the survival probability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A generalized Weyl relation approach to the time operator and its connection to the survival probability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generalized Weyl relation approach to the time operator and its connection to the survival probability will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-598697