# Equilibrium particle states in weakly open dynamics. (arXiv:1904.06338v1 [quant-ph])

The construction of the stationary states of a one dimensional particle

moving freely or in the presence of a Dirac delta potential is an elementary

exercise in quantum mechanics. This problem is generalized in this work for

open dynamics where the stationary reduced density matrix is found by solving a

master equation, derived for weak test particle-environment interactions. The

goal is to assess the effects of decoherence and dissipative forces on the

equilibrium state, with special attention payed to universal relations,

obtained in the infinitesimal system-environment interaction limit. The pure

plane waves are generalized into two directions, to propagating and to

tunneling states, by constructing the desired representations of translations.

The relaxed bound states of the Dirac delta potential cover a large class of

states and the adiabatic turning on the environment interactions is used to

find the relaxed final state of the usual pure bound state. The spread of the

wave packet is studied by the help of the probability distribution of the

coordinate and the probability flux and some fingerprints of the environment

are pointed out.