arXiv subjects
Publications and source records attributed to Stephen B. Sontz.
We show (an earlier conjecture of the last two authors) that the momentum and position operators of mu-deformed quantum mechanics for -1/2 < mu < 0 are not Accardi complementary. We also prove some related formulas that were conjectured by the same authors.
In this note we show that the momentum and position operators of $μ$-deformed quantum mechanics for $μ> 0$ are not Accardi complementary in a sense that we will define. We conjecture that this is also true if $-1/2 < μ< 0$.
We consider a $μ$-deformation of the Segal-Bargmann transform, which is a unitary map from a $μ$-deformed quantum configuration space onto a $μ$-deformed quantum phase space (the $μ$-deformed Segal-Bargmann space). Both of these Hilbert spaces have canonical orthonormal bases. We obtain explicit formulas for the Shannon entropy of some of the elements of these bases. We also consider two reverse log-Sobolev inequalities in the $μ$-deformed Segal-Bargmann space, which have been proved in a previous work, and show that a certain known coefficient in them is the best possible.