  In quantum mechanics, the Rosen-Zener model represents a two-level quantum
system. Its generalization to multiple degenerate sets of states leads to
larger non-autonomous linear system of ordinary differential equations (ODEs).
We propose a new method for computing the solution operator of this system of
ODEs. This new method is based on a recently introduced expression of the
solution in terms of an infinite matrix equation, which can be efficiently
approximated by combining truncation, fixed point iterations, and low-rank
approximation. This expression is possible thanks to the so-called
$\star$-product approach for linear ODEs. In the numerical experiments, the new
method's computing time scales linearly with the model's size. We provide a
first partial explanation of this linear behavior.
