Related papers: Remarks on the notion of quantum integrability
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
Integrability in quantum theory has been defined in more than one ways. Recently, Braak suggested a new definition that a quantum system is integrable if the number of parameters required to specify the eigenstates and the number degrees of…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
We give a sufficient condition for quantising integrable systems.
The concept and the formalization of the arrival time in quantum mechanics are discussed. Different approaches based on trajectories, quantization rules, time operators, phase space techniques, renewal equations or operational procedures…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
An attempt is made to formulate quantum mechanics (QM) in physical rather than in mathematical terms. It is argued that the appropriate conceptual framework for QM is "contextual objectivity", which includes an objective definition of the…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
I discuss various aspects of the concept of a quantity in physics and metrology and related consideration in reference documents of IUPAP, IUPAC, ISO, IEC, and JCGM.