Quantum mechanics using two auxiliary inner products
arXiv:2110.12155 · doi:10.1016/j.physleta.2021.127792
Abstract
The current applications of non-Hermitian but symmetric Hamiltonians cover several, mutually not too closely connected subdomains of quantum physics. Mathematically, the split between the open and closed systems can be characterized by the respective triviality and non-triviality of an auxiliary inner-product metric . With our attention restricted to the latter, mathematically more interesting unitary-evolution case we show that the intuitive but technically decisive simplification of the theory achieved via an "additional" symmetry constraint upon can be given a deeper mathematical meaning via introduction of a certain second auxiliary inner product.
16 pp