Mathematical Foundations of Time Asymmetric Quantum Mechanics

Quantum Fest 2016 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics

Gadella, M.^1

Departamento de Física Teórica, Atómica y Optica. Facultad de Ciencias, Universidad de Valladolid, Paseo Belén 7, Valladolid

47011, Spain^1

关键词: Half-planes;    Mathematical foundations;    Mathematical tools;    Quantum scattering;    Resonance scattering;    Rigged Hilbert space;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/839/1/012001/pdf
DOI  :  10.1088/1742-6596/839/1/012001

来源: IOP

【 摘 要 】

We review the mathematical tools that are suitable for a formulation of time asymmetry in quantum mechanics. In particular, Hardy functions on a half plane and rigged Hilbert spaces constructed with a subclass of Hardy functions. This time asymmetry often appears in quantum scattering and, in particular, in resonance scattering. We review the construction of Gamow vectors, often considered Gamow states for resonances. A brief summary of the fundamental ideas of time asymmetric quantum mechanics is presented in a last section.