The Non-Hermitian quantum mechanics and its canonical structure
Quantum Physics
2020-05-22 v1
Abstract
The non-Hermitian Schr\"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. Its quantization called non-Hermitian quantum field theory is discussed. By virtue of the canonical equation, the theory of non-Hermitian quantum mechanics is totally reformulated, including the probability amplitudes of states, the expectations of operators, as well as the expressions of interaction terms. The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation. Specifically, the imaginary parts the non-Hermitian eigenenergy and adiabatic geometric phase are actually unphysical, although they are mathematically perfect.
Keywords
Cite
@article{arxiv.2005.10474,
title = {The Non-Hermitian quantum mechanics and its canonical structure},
author = {Qi Zhang},
journal= {arXiv preprint arXiv:2005.10474},
year = {2020}
}