Related papers: Observables and States p-Mechanics
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
A general scheme to seek for the relations between entanglement and bservables is proposed in principle. In two-qubit systems with enough general Hamiltonian, we find the entanglement to be the functions of observables for six kinds of…
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…
We describe a construction of wavelets (coherent states) in Banach spaces generated by ``admissible'' group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an…
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. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the…
Second degree polynomial Heisenberg algebras are realized through the harmonic oscillator Hamiltonian, together with two deformed ladder operators chosen as the third powers of the standard annihilation and creation operators. The…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory (PCSFT). The correspondence between classical…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
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…
We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is…
We demonstrate how different types of $SU(3)$ Heisenberg models can be implemented with the use of the $p$ orbitals of three dimensional optical lattices. By considering a Mott insulator with unit filling, the dynamics is well described by…
We explore the sense in which the state of a physical system may or may not be regarded (an) observable in quantum mechanics. Simple and general arguments from various lines of approach are reviewed which demonstrate the following no-go…