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We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in…
Considerable attention has been recently focused on quantum-mechanical systems with boundaries and/or singular potentials for which the construction of physical observables as self-adjoint (s.a.) operators is a nontrivial problem. We…
In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival…
In this paper we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them in particular with a number of different (but equivalent) families of…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We address the joint estimation of changes in the position and linear momentum of a quantum particle or, equivalently, changes in the complex field of a bosonic mode. Although these changes are generated by non-commuting operators, we show…
In this paper we study the self-adjoint and co-isometry composition and weighted composition operator on $H_E(\zeta).$ We also discuss the conditions under which adjoint operator of a composition and weighted composition operator on…
We study the momentum operator defined on the disjoint union of two intervals. Even in one dimension, the question of two non-empty open and non-overlapping intervals has not been worked out in a way that extends the cases of a single…
In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schr\"{o}dinger representation (working often with the innovative and heuristically productive concept of ${\cal PT}-$symmetry), it is demonstrated…
Let $q\neq \pm 1$ be a complex number of modulus one. This paper deals with the operator relation $AB=qBA$ for self-adjoint operators $A$ and $B$ on a Hilbert space. Two classes of well-behaved representations of this relation are studied…
In this paper, we give a description of the spectrum of a class of non-selfadjoint perturbations of selfadjoint operators in dimension one and we show that it is given by Bohr-Sommerfeld quantization conditions. To achieve this, we make use…
A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation…
For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions), the corresponding…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
In biorthogonal quantum mechanics, the eigenvectors of a quasi-Hermitian operator and those of its adjoint are biorthogonal and complete and the probability for a transition from a quantum state to any one of these eigenvectors is positive…
The aim of the paper is to study the question whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator $\cal H$. The eigenfunctions…
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…