Transition Decomposition of Quantum Mechanical Evolution
Abstract
We show that the existence of the family of self-adjoint Lyapunov operators introduced in [J. Math. Phys. 51, 022104 (2010)] allows for the decomposition of the state of a quantum mechanical system into two parts: A past time asymptote, which is asymptotic to the state of the system at t goes to minus infinity and vanishes at t goes to plus infinity, and a future time asymptote, which is asymptotic to the state of the system at t goes to plus infinity and vanishes at t goes to minus infinity. We demonstrate the usefulness of this decomposition for the description of resonance phenomena by considering the resonance scattering of a particle off a square barrier potential. We show that the past time asymptote captures the behavior of the resonance. In particular, it exhibits the expected exponential decay law and spatial probability distribution.
Cite
@article{arxiv.1101.4180,
title = {Transition Decomposition of Quantum Mechanical Evolution},
author = {Y. Strauss and J. Silman and S. Machnes and L. P. Horwitz},
journal= {arXiv preprint arXiv:1101.4180},
year = {2015}
}
Comments
Accepted for publication in Int. J. Theor. Phys