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The main goal of this work is to provide a description of the {trace per unitvolume} in terms of the {Dixmier trace} (regularized by the resolvent of theharmonic oscillator) for a large class of two-dimensional \emph{magneticoperators} perturbed by (homogeneous) {potentials}. One of the payoffs of thisresult is the possibility of reinterpreting the {density of states} (DOS) ofthese perturbed magnetic systems via the {Dixmier trace}, and taking advantageof the fact that this quantity can be conveniently calculated on the basis ofthe Laguerrre functions that diagonalize the harmonic oscillator.

Dixmier trace and the DOS of perturbed magnetic operators