Related papers: Identification of the metric for diagonalizable (a…
Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones. Compared with the way…
Among ${\cal P}$-pseudo-Hermitian Hamiltonians $H ={\cal P}^{-1} H^\dagger \cal P}$ with real spectra, the ''weakly pseudo-Hermitian" ones (i.e., those employing non-self-adjoint ${\cal P} \neq {\cal P}^\dagger$) form a remarkable…
Starting with the modified Dirac equations for free massive particles with the $\gamma_5$-extension of the physical mass $m\rightarrow m_1 + \gamma_5 m_2$, we consider equations of relativistic quantum mechanics in the presence of an…
A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a…
$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This…
To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…
The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the…
We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like…
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of…
The quantum-field model described by non-Hermitian, but a ${\cal PT}$-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value $m \leq m_{max}= {m_1}^2/2m_2$ takes place for the case…
We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary…
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…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
We consider the problem of designing a variety of "system guided" basis sets for quantum mechanical anharmonic oscillators. Using ideas based on supersymmetric quantum mechanics, we design canonical transformations of the usual position and…
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an…
Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{PT}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of…
We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is…
For an invertible (bounded) linear operator Q acting in a Hilbert space ${\cal H}$, we consider the consequences of the QT-symmetry of a non-Hermitian Hamiltonian $H:{\cal H}\to{\cal H}$ where T is the time-reversal operator. If H is…
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.…
A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge"…