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4-level oscillator babilities calculation of transition classical calculations CLASSICAL ENERGY TRANSFERRED classical motion classical oscillator classical problem classical result classical trajectory cm/sec colliding particle correct quantum mechanical departure dependent diatomic molecule discussed in Ref energy is identical expand the solution EXPONENTIAL FORCING first-order perturbation forced harmonic oscillator forced-harmonic-oscillator solution form of Eq given in Eq high energy collisions higher order incident particle interacting force interaction potential Kerner LINEAR FORCING POTENTIAL MOLECULAR COLLISIONS momentum wave functions Multi-quantum transitions NUMERICAL SOLUTION order potential oscillating wave functions oscillating wave packet oscillator coordinate oscillator driven oscillatory wave functions perturbation calculation perturbation result perturbation treatment present paper purely time-dependent quantum mechanical result quantum mechanical solution Rapp and Sharp Schrbdinger equation Schrddinger second potential shown in Fig simple harmonic oscillator taken equal time-dependent force time-dependent potential transition probabilities given transition probabilities obtained transitions between stationary velocities VIBRATIONAL ENERGY TRANSFER vibrational relaxation wave function given