2017/07/20 by Mustapha Maamache, Maamache, Mustapha
Physics and Astronomy · #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1707.06392
openalex publication_date 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary evolution, and collecting the basic results around it and postulating the norm preserving. This cautionary postulate imposing that the time evolution of a non Hermitian quantum system preserves the inner products between the associated states must not be read naively. We also give an example showing that the solutions of time-dependent non Hermitian Hamiltonian systems given by a linear combination of SU(1,1) and SU(2) are obtained thanks to time-dependent non-unitary transformation.