The operator to approximate is with the maximal and minimal eigenvectors , , .
This means the factor is a phase factor, and hence
with the Bessel function of first kind of order (the proof for this expression is to be found in in appendix 4.2).typeset@protect @@footnote SF@gobble@opt These formulas were occasionally faulty in some of the papers I am citing.
The coefficients go to zero exponentially as becomes greater than so the method is very fast except for very short times where this exponentially decaying tail becomes dominant in the calculation time.
The same result is produced by