8 citations · 15 across the 3 of their papers we have counts for
5 papers
Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator
Gilles Regniers, Joris Van der Jeugt
In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and th…
Wigner quantization of some one-dimensional Hamiltonians
Gilles Regniers, Joris Van der Jeugt
Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have bee…
The Hamiltonian H=xp and classification of osp(1|2) representations
G. Regniers, J. Van der Jeugt
The quantization of the simple one-dimensional Hamiltonian H=xp is of interest for its mathematical properties rather than for its physical relevance. In fact, the Berry-Keating co…
Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matrix
Gilles Regniers, Joris Van der Jeugt
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian des…
Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction
G. Regniers, J. Van der Jeugt
We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled by a nearest neighbour interaction of the form ( refers to the positi…