  This paper is an extension of Fujii et al (quant--ph/0307066) and in this one
we again treat a model of atom with n energy levels interacting with n(n-1)/2
external laser fields, which is a natural extension of usual two level system.
Then the rotating wave approximation (RWA) is assumed from the beginning.
  To solve the Schr{\" o}dinger equation we set the {\bf consistency condition}
in our terminology and reduce it to a matrix equation with symmetric matrix $Q$
consisting of coupling constants.
  However, to calculate $\exp(-itQ)$ {\bfexplicitly} is not easy. In the case
of three and four level systems we determine it in a complete manner, so our
model in these levels becomes realistic.
  In last, we make a comment on Cavity QED quantum computation based on three
energy levels of atoms as a forthcoming target.
