Effective Hamiltonian Approach to the Master Equation

A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The effective Hamiltonian governing the time evolution of the composed system are derived from the master equation. Two examples, the dissipative two-level system and the damped harmonic oscillator, are presented to illustrate the solving procedure. PACS number(s): 05.30.-d, 05.40.+j, 42.50.Ct