Quantal master equation valid for any time scale

A new memoryless expression for the equation of motion for the reduced density matrix is derived. It is equivalent to that proposed by Tokuyama and Mori, but has a more convenient form for the application of the perturbational expansion method. The master equation derived from this form of equation in the first Born approximation is applied to two examples, the Brownian motion of a quantal oscillator and that of a spin. In both examples the master equation is rewritten into the coherent-state representation. A comparison is made with the stochastic theory of the spectral line shape given by Kubo, and it is shown that this theory of the line shape can be incorporated into the framework of the present theory.