Pseudo-Hermitian Representation of Quantum Mechanics

Understand

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly.

• We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject.
• We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study.
• We then offer a survey of the necessary mathematical tools and elaborate on a number of relevant issues of fundamental importance.