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The space-time method is applied to a model system-the Simple HarmonicOscillator in a laser field to simulate the Stimulated Raman Adiabatic Passage(STIRAP) process. The Space-Time method is a computational theory firstintroduced by Weatherford et. al. to solve Time-Dependent Systems with oneboundary value and applied to electron spin system with invariant Hamiltonian[Journal of Molecular Structure {\bf 592} 47]. The implementation in thepresent work provides an efficient and general way to solve the Time-DependentSchr{\"o}dinger Equation and can be applied to multi-state systems. Thealgorithm for simulating the Simple Harmonic Oscillator STIRAP can be appliedto solve STIRAP problems for complex systems.

Application of the Space-Time Method to Stimulated Raman Adiabatic Passage on the Simple Harmonic Oscillator