@article{oai:ynu.repo.nii.ac.jp:00007027, author = {Fujii, Kazuyuki}, issue = {1}, journal = {Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学}, month = {}, note = {application/pdf, In this paper we show how to calculate explicitly the exponential of certain matrices, which are evolution operators governing the interaction of the four level system of atoms and the radiation, etc. We present a consistent method in terms of the magic matrix by Makhlin. As a closely related subject, we derive a closed form expression of the Baker-Campbell-Hausdor formula for a class of matrices in $SU(4)$ , by use of the method developed by the present $author8$ in $quant-ph/0610009$.}, pages = {31--44}, title = {EXPONENTIATION OF CERTAIN MATRICES RELATED TO THE FOUR LEVEL SYSTEM BY USE OF THE MAGIC MATRIX}, volume = {54}, year = {2007} }