The Unboundedness of Quantum-Mechanical Matrices

S. G. Eckstein, B. B. Varga, S. Ø. Aks

CHANGSOO BAHN, Chul Ki Ko, Yong‐Moon Park

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad-type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola's sufficient conditions for conservativity [1] to show that the semigroups are conservative. We then apply our results to a quantum mechanical system.

Stanley Gudder, Vladimir Naroditsky

Debashish Goswami, Kalyan B. Sinha

Brian D. Josephson

Fabio Bagarello, J.P. Gazeau, Franciszek Hugon Szafraniec +1 more

Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics