Related papers: Quantization of the canonically conjugate pair ang…
Optical fields provide an accessible platform to explore connections between classical and quantum mechanics. We introduce a group-theoretic framework based on the $\mathrm{su}(1,1)$ Lie algebra to construct classical analogs of…
We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle $\phi $ and its canonical moment $L_{z}$. We illustrate our results with analytical examples.
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component $\phi_j$ of the wave vector is understood as a…
We reconsider quantum mechanical systems based on the classical action being the period of a one form over a cycle and elucidate three main points. First we show that the prepotenial V is no longer completely arbitrary but obeys a…
A simple argument is presented that explicitly shows how to construct an arbitrary quantum gate acting on orbital angular momentum (OAM) of single photons. The scheme can be applied to implement subspace multiplexing, where a single…
In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of…
One of the most widely used techniques for measuring the orbital angular momentum components of a light beam is to flatten the spiral phase front of a mode, in order to couple it to a single-mode optical fiber. This method, however, suffers…
We briefly review the recent progress of theories and experiments on spin-orbital-angular-momentum (SOAM)-coupled quantum gases. The coupling between the intrinsic degree of freedom of particles and their external orbital motions widely…
Cavity optomechanical system involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
For a particle moving on a half-line or in an interval the operator $\hat p = - i \partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on $\hat p$ fails. Based upon a…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
We propose a quasi-periodic structure (QPS) with topological defects. The analytical expression of the corresponding Fourier spectrum is derived, which reflects the combined effects of topological structure and quasitranslational symmetry.…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
Hybrid entangled states exhibit entanglement between different degrees of freedom of a particle pair and thus could be useful for asymmetric optical quantum network where the communication channels are characterized by different properties.…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…