# 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.