Dissipation in quantum mechanics

[hokhani]

In classical mechanics potential is defined for conservative forces and dissipative forces such as friction don't have potential. In quantum mechanics, Schrödinger equation which includes a potential, deals with problems. How can one treat the dissipative forces in quantum mechanics?

 

[Demystifier]

There are several methods one may use.

The most popular method is to consider the system as an open system, described not by a pure state (wave function) but by a mixed density matrix. For more details see
http://en.wikipedia.org/wiki/Open_quantum_system
http://en.wikipedia.org/wiki/Lindblad_equation

Some basics of methods for open quantum systems can even be found in some general textbooks on QM, such as
https://www.amazon.com/dp/052187534X/?tag=pfamazon01-20
https://www.amazon.com/dp/0521869633/?tag=pfamazon01-20Another (but related) method is to consider your dissipative system as a part of a larger system, such that the larger system is a non-dissipative one. Unfortunately, the method may depend on how exactly you enlarge your original dissipative system.A completely different, more abstract method, is by using Weyl quantisation:
http://lanl.arxiv.org/abs/quant-ph/0311159