相关论文: Duality and Conditional Expectations in the Nakaji…

A new representation -which is similar to the Bargmann representation- of the creation and annihilation operators is introduced, in which the operators act like "multiplication with" and like "derivation with respect to" a single real…

This paper completes a previous work by constructing a class of positive-energy relativistic spatial localization observables in Minkowski spacetime within quantum field theory, using the stress-energy-momentum tensor smeared with suitable…

Our goal is the discussion of the problem of mathematical interpretation of basic postulates (or `principles') of Quantum Mechanics: transitions to quantum stationary orbits, the wave-particle duality, and the probabilistic interpretation,…

Sufficient and necessary conditions are presented for the existence of $(N,M)$-positive operator valued measures ($(N,M)$-POVMs) valid for arbitrary-dimensional quantum systems. A sufficient condition for the existence of $(N,M)$-POVMs is…

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but…

In this paper I argue against Carcassi, Calderon, and Aidala's recent claim that the Hilbert spaces are unphysical and should be replaced with the Schwartz spaces in quantum mechanics, since Hilbert spaces include states with infinite…

Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…

We represent in this note the solutions of the electronic Schr\"odinger equation as traces of higher-dimensional functions. This allows to decouple the electron-electron interaction potential but comes at the price of a degenerate elliptic…

We study the operator formulation of classical mechanics by explicitly applying it to two central potentials in 2 dimensions. After constructing the classical Hamiltonian operators and corresponding Schr\"odinger like equations, we solve…

We construct projective limit of projective sequence in the following categories: Archimedean order unit spaces with unital positive maps and operator systems with unital completely positive maps. We prove that inductive limit and…

Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…

An abstract formulation of quantum dynamics in the presence of a general set of quantum constraints is developed. Our constructive procedure is such that the relevant projection operator onto the physical Hilbert space is obtained with a…

Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values…

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…

We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective…

It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…

This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two(many)-particle, `explicitly correlated' basis representation, necessary for…

Zurek's existential interpretation of quantum mechanics suffers from three classical prejudices, including the belief that space and time are intrinsically and infinitely differentiated. They compel him to relativize the concept of…

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…

The paper is concerned with the following question: if $A$ and $B$ are two bounded operators between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, and $\mathcal{M}$ and $\mathcal{N}$ are two closed subspaces in $\mathcal{H}$, when will…