The Swanson's Hamiltonian H (cf. eq. (1)) as proposed in ref. [10]
is a remarkable solvable ``next-to-harmonic-oscillator" quantum
model which proves self-adjoint (as necessary) in many different
nontrivial Hilbert spaces (sampled in ref. [9]). C. Quesne points
out that the feasibility of an explicit and exact construction of
at least some of these ``physical" Hilbert spaces becomes a more
or less trivial consequence of an application of a suitable ansatz
and of the Baker-Campbell-Hausdorff formulae. The core of the idea
is that H can be understood as a mere linear superposition of
three generators of su(1,1) in a specific representation. This
enables C. Quesne to conclude that also any other selection of the
specific representation of su(1,1) would lead to another tractable
generalized Swanson Hamiltonian. She lists several explicit
examples for illustration, incorporating some differential single-
and multi-particle oscillators (of a generalized Calogero type) as
well as some new, non-standard multiboson models mimicking
absorbtion/emission in nonlinear media.

MR2344511 Quesne, C. A non-Hermitian oscillator Hamiltonian and ${\rm su}(1,1)$: a way towards generalizations. J. Phys. A 40 (2007), no. 30, F745--F751. 81Q10