Related papers: Reply to Comment on ``Time-dependent quasi-Hermiti…
In arXiv:0710.5653v1 M. Znojil claims that he has found and corrected an error in my paper: [Phys. Lett. B \textbf{650}, 208 (2007), arXiv:0706.1872v2] and that it is possible to escape its main conclusion, namely that the unitarity of the…
We show that the consequences of an introduction of a manifest time-dependence in a pseudo-Hermitian Hamiltonian H=H(t) are by far less drastic than suggested by A. Mostafazadeh in Phys. Lett. B 650 (2007) 208 (arXiv:0706.1872v2…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary evolution, and collecting the basic…
It is shown that the paper "Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential", by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a…
In a recent paper [Phys. Rev. A 61, 022117 (2000)], quant-ph/9906034, A. Peres argued that quantum mechanics is consistent with special relativity by proposing that the operators that describe time evolution do not need to transform…
The basic requirement that, in quantum theory, the time-evolution of any state is determined by the action of a unitary operator, is shown to be the underlying cause for certain ``exact'' results which have recently been reported about the…
In the paper "Observation of Fast Evolution in Parity-Time-Symmetric System" the authors propose a physical apparatus for the realization of a faster than Hermitian evolution. This last appears in contrast with the conclusions obtained in…
We explain why the main conclusion of Bender et al, hep-th/0511229 [J. Phys. A 39 (2006) 1657] regarding the practical superiority of the non-Hermitian description of PT-symmetric quantum systems over their Hermitian description is not…
With the aim to solve the time-dependent Schr\"{o}dinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent $\mathcal{PT}$-symmetric one.…
Update: A time-independent $n\times n$ PT-symmetric (and symmetric) Hamiltonian is diagonalizable since it has all distinct real eigenvalues and the resulting diagonal matrix is a real symmetric matrix. The diagonalization results an…
In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
In this brief comment we attempt to clarify the apparent discrepancy between the papers [1] and [2] on the quantum brachistochrone, namely whether it is possible to use a judicious mixture of Hermitian and non-Hermitian quantum mechanics to…
We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…