PT-symmetric quantum mechanics is a Hermitian quantum mechanics

2013/12/30 by Lee, Sungwook
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1312.7738

Abstract

The author discusses a different kind of Hermitian quantum mechanics, called J-Hermitian quantum mechanics. He shows that PT-symmetric quantum mechanics is indeed J-Hermitian quantum mechanics, and that time evolution (in the Krein space of states) is unitary if and only if Hamiltonian is J-Hermitian (or equivalently PT-symmetric). An issue with unitarity comes up when time evolution is considered in the Hilbert space of states rather than in the Krein space of states. The author offers possible scenarios with this issue.

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