Related papers: A coherent state associated with shape-invariant p…
Shape Dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable form classical General Relativity. If taken seriously, it suggests that the spacetime--geometry picture that underlies…
We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "the algebra of supersymmetric quantum mechanics", and its Fock representation. The model…
Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the…
Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent…
In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…
We prove a quantitative stability result for the Heisenberg-Pauli-Weyl inequality. This yields next and next-to-next order correction terms, sharpening the inequality in all dimensions.
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…
We consider the semiclassical Schroedinger operator with a "well in an island" potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
Metric-affine geometry provides a non-trivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the space-time (with non-vanishing torsion and…
We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$ matrix should be invariant under field redefinitions, and hence can be represented by the…
The Heisenberg-Weyl group $HW(d)$ related to a $d$-dimensional Hilbert space $H(d)$, is enlarged into the Heisenberg-Weyl-parity group $HWP(d)$ that incorporates parity transformations. It consists of $2d^3$ elements, of which $d^3$…
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by…
A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part…
In this work we describe semiclassical states in graphene under a constant perpendicular magnetic field by constructing coherent states in the Barut-Girardello sense. Since we want to keep track of the angular momentum, the use of the…
The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group…