The Non-Hermitian quantum mechanics and its canonical structure
- URL: http://arxiv.org/abs/2005.10474v1
- Date: Thu, 21 May 2020 05:52:53 GMT
- Title: The Non-Hermitian quantum mechanics and its canonical structure
- Authors: Qi Zhang
- Abstract summary: The non-Hermitian Schr"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation.
The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation.
- Score: 7.784991832712813
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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