Related papers: Quantum oscillator as 1D anyon
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
We show that the quantum dynamics of a real scalar field for a large class of potentials in the symmetric Gaussian state, where the nonperturbative quantum contributions are taken into account, can be described equivalently by a…
It is shown that $U(1)$--Hamiltonian reduction of a four--dimensional isotropic quantum oscillator results in a bound system of two spinless Schwinger's dyons. Its wavefunctions and spectrum are constructed.
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM) is showed to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this…
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds…
At the primary level of reality as described by quantum field theory, a fundamental particle like an electron represents a stable, discrete, propagating excited state of its underlying quantum field. QFT also tells us that the lowest vacuum…
We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a {\delta} potential barrier. The dipole or quadrupole moment is represented…
The quadrature distribution for the quantum damped oscillator is introduced in the framework of the formulation of quantum mechanics based on the tomography scheme. The probability distribution for the coherent and Fock states of the damped…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
One of the interesting fundamental phenomenon which was observed in the last decades is the discovery of anyons, relativistic spinning particles in $2+1$ dimensions. In contrast to three-dimensional space, indistinguishable quantum…
We investigate the quantum dynamics of a quantum oscillator coupled with the most upper state of a three-level $\Lambda-$ type system. The two transitions of the three-level emitter, possessing orthogonal dipole moments, are coherently…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
We outline the nonlinear transformation in the path integral representation for partition function of O(N) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This…
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su_q(2). The spectrum of position in this discrete…
A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time…
The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an…
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the…
Quantum-mechanical WKB-method is elaborated for the known quantum oscillator problem in curved 3-spaces models Euclid, Riemann, and Lobachevsky E_{3}, H_{3}, S_{3} in the framework of the complex variable function theory. Generalized…