Related papers: Is Weak Pseudo-Hermiticity Weaker than Pseudo-Herm…
We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such…
We extend the definition of eta-weak-pseudo-Hermiticity to the class of potentials endowed with position-dependent mass. The construction of non-Hermitian Hamiltonians through some generating function are obtained. Special cases of…
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in…
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum…
It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an…
In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a…
"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $\eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $\eta$ operators. We show…
The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction with the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the…
We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…
Pseudo-Hermitian operators generalize the concept of Hermiticity. This class of operators includes the quasi-Hermitian operators, which reformulate quantum theory while retaining real-valued measurement outcomes and unitary time evolution.…
We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis…
Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…