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Summary form only given.The adiabatic passage techniques, via controlled temporal variation of elements of Hamiltonian, offer some possibility of producing complete population transfer. The stimulated Raman adiabatic passage (STIRAP) is the most remarkable example of an adiabatic passage technique. In this paper, we examine an important aspect of STIRAP procedure in magnetic sublevel structure with degenerate initial states. It is our purpose to find procedures that allow selective transfer into different magnetic sublevels selected simply by tuning the laser frequencies. We illustrate the possibilities by examining in detail a particular case, D/sub 1/ line of /sup 87/Rb atoms with degenerate initial state interacting with linearly polarized lasers. The time-dependent Schrodinger equation can describe the population transfer that occurs during a much shorter time interval than the lifetime for spontaneous emission from intermediate states. Under the rotating-wave approximation (RWA), the Schrodinger equation is rearranged into a set of coupled first-order differential equations for the slowly varying components of state vector. The coupled differential equations are numerically solved using the implicit differencing algorithm that is especially useful for a stiff set of coupled differential equations. The RWA Hamiltonians are derived according to the polarization directions of the fields and to the initial state. It is the most characteristic feature of STIRAP with the degenerate initial states that the different RWA Hamiltonians, consequently different coupled differential equations, should be used according to the initial state.