Related papers: Self-adjointness in Quantum Mechanics: a pedagogic…
A non-Hermitian operator may serve as the Hamiltonian for a unitary quantum system, if we can modify the Hilbert space of state vectors of the system so that it turns into a Hermitian operator. If this operator is time-dependent, the…
We analyze a general family of position-dependent mass quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a…
While quantum mechanics allows spooky action at a distance at the level of the wave-function, it also respects locality since there is no instantaneous propagation of real physical effects. We show that this feature can be proved in the…
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…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
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…
The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
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…
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…
Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…
Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence…
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…
We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i)…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…