in the recent paper [Journal of Physics A, 43474-0288 (2011)], B. Helffer and
R. Purice compute the second term of a semi-classical trace formula for a
Schr\"odinger operator with magnetic field. We show how to recover their
formula by using the methods developped by the geometers in the seventies for
the heat expansions.Comment: To appear in "Analysis of Partial Differential Equations