Semi-groups and time operators for quantum unstable systems
Abstract
We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely exponentially decaying states that correspond to complex eigenvalues of this semi-group. The construction provides a probabilistic interpretation of the resonant states characterized in terms of the Hardy class.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.