Related papers: Comment on Complex Extension of Quantum Mechanics
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…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of…
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…
In standard quantum mechanics (QM), a state vector $| \psi \rangle$ may belong to infinitely many different orthogonal bases, as soon as the dimension $N$ of the Hilbert space is at least three. On the other hand, a complete physical…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
Quantum covariant Hamiltonian system theory provides a coherent framework for modelling the complex dynamics of quantum systems. In this paper, we centrally deal with the Hermiticity of quantum operators that directly links to the physical…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
Quantum Mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
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…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this…
With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the…
One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum…