Hybrid form of quantum theory with non-Hermitian Hamiltonians

In Schrödinger picture the unitarity of evolution is usually guaranteed by Hermiticity Hamiltonian operator h=h† in a conventional Hilbert space Htextbook. After Dyson-inspired operator-transformation (OT) non-unitary preconditioning ?:h?H simplified H is, its manifestly unphysical Hauxiliary, non-Hermitian. Besides natural OT-based physical interpretation it can also be “Hermitized” (i.e., made compatible with unitarity) via metric-amendment (MA) change space, Hauxiliary?Hphysical. our present letter we propose another, third, hybrid form (HF) Hermitization which involves, simultaneously, both and metric. Formally this means that original Dyson map assumed factorizable, ?=?M?H. A key practical advantage new HF approach lies model-dependent adaptability such factorization. The flexibility possible optimality balance between MA-related metric-amending) factor ?M OT-related Hamiltonian-changing) ?H are explicitly illustrated an elementary two-state quantum model.