23 citations · 97 across the 14 of their papers we have counts for
14 papers
On spacetime algebra and its relations with negative masses
N. Debergh, J. -P. Petit
We consider four subsets of the complexified spacetime algebra, namely the real even part, the real odd part, the imaginary even part and the imaginary odd part. This naturally lea…
On evidence for negative energies and masses in the Dirac equation through a unitary time-reversal operator
Nathalie Debergh, Jean-Pierre Petit, Gilles D'Agostini
We review the standards of relativistic quantum mechanics such as the Dirac equation under the concept of negative masses. We show that negative energies are acceptable provided th…
On supersymmetries in nonrelativistic quantum mechanics
J. Beckers, N. Debergh, A. G. Nikitin
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generat…
Quasi exactly solvable quantum lattice solitons
Y. Brihaye, N. Debergh, A. Nininahazwe
We extend the exactly solvable Hamiltonian describing quantum oscillators considered recently by J. Dorignac et al. by means of a new interaction which we choose as quasi exact…
Polynomial deformations of sl(2,R) in a three-dimensional invariant subspace of monomials
N. Debergh, J. Ndimubandi, B. Van den Bossche
New finite-dimensional representations of specific polynomial deformations of sl(2,R) are constructed. The corresponding generators can be, in particular, realized through linear d…
Darboux transformations for quasi-exactly solvable Hamiltonians
N. Debergh, Boris F. Samsonov, B. Van Den Bossche
We construct new quasi-exactly solvable one-dimensional potentials through Darboux transformations. Three directions are investigated: Reducible and two types of irreducible second…