  The understanding of nonlinear PT-symmetric quantum systems, arising for
example in the theory of Bose-Einstein condensates in PT-symmetric potentials,
is widely based on numerical investigations, and little is known about generic
features induced by the interplay of PT-symmetry and nonlinearity. To gain
deeper insights it is important to have analytically solvable toy-models at
hand. In the present paper the stationary states of a simple toy-model of a
PT-symmetric system are investigated. The model can be interpreted as a simple
description of a Bose-Einstein condensate in a PT-symmetric double well trap in
a two-mode approximation. The eigenvalues and eigenstates of the system can be
explicitly calculated in a straight forward manner; the resulting structures
resemble those that have recently been found numerically for a more realistic
PT-symmetric double delta potential. In addition, a continuation of the system
is introduced that allows an interpretation in terms of a simple linear matrix
model.
