A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the coordinate and momentum dispersions of the particle are derived. A new dissipative Schrödinger equation is proposed and solved for particular cases. A new dissipative Liouville equation is heuristically constructed.
Key words: quantum Brownian motion, dissipative Schrödinger and Liouville equations
Topic: CHEMISTRY