Related papers: On Quantization of Polynomial Momentum Observables
Position-momentum entanglement is a versatile high-dimensional resource in quantum optics. From fundamental tests of reality, to application in quantum technologies, spatial entanglement has had an increasing growth in recent years. In this…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
The review is devoted to topological global aspects of quantal description. The treatment concentrates on quantizations of kinematical observables --- generalized positions and momenta. A broad class of quantum kinematics is rigorously…
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…
This talk is a survey of the question of joint measurability of coexistent observables and its is based on the monograph Operational Quantum Physics [1] and on the papers [2,3,4].
The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…
Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…
For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…
We study the quantization of a model proposed by Newton to explain centripetal force namely, that of a particle moving on a regular polygon. The exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a particle moving…
We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable.
In quantum mechanics, the measureable quantities of a given theory are predicted by performing a weighted sum over possibilities. We show how to arrange the possibilities into bundles such that the associated subsums can be viewed as…
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
In this paper we give the Bohr-Sommerfeld-Heisenberg quantization of the mathematical pendulum.
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…