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Quantum Particle Subject to Impulsive Collisions

The effects of strong impulsive collisions on the time evolution of a quantum particle are studied. A general formalism is proposed in which a given collision effectively randomizes the momentum of the particle while leaving the position of the particle unchanged. This is then applied to a damped harmonic oscillator. It is explicitly shown that a Gaussian wave packet approaches equilibrium at t → ∞. Relations to macroscopic quantum coherence are discussed.