Institute for Applied Mathematics (IfAM) Activities Talks
Seminar Analysis and Theoretical Physics

Seminar Analysis and Theoretical Physics

Talk on Tuesday, January 10, 2023, at 3 p.m., room c311, main building of the university; Prof. Dr. Reinhard F. Werner, LUH, Incomplete quantum dynamics

Incomplete quantum dynamics

 

Normally, the time evolution in quantum mechanics is given by a unitary one-parameter group. In this talk about an ongoing project, I am pursuing a natural generalization in which a particle may escape to infinity in finite time. A prototype is a classical particle in one dimension with an x3-potential. This confirms the intuitive connection between classical incompleteness and selfadjointness. From the classical analogy it is natural to modify the dynamics to a contraction semigroup. This can either be obtained by the dissipative branch of von Neumann’s extension theory, or by a Trotter limit in the weak operator topology, by which the sum of selfadjoint operators may sometimes be well-defined, but fail to be selfadjoint. For the cubic potential, an approach based on Nelson’s regularization of path integrals yields a specific contraction semigroup.