  This paper discusses the energy optimal control problem for the class of
quantum systems that possess dynamical symmetry of SU(1,1), which are widely
studied in various physical problems in the quantum theory. Based on the
maximum principle on Lie group, the complete set of optimal controls are
analytically obtained, including both normal and abnormal extremals. The
results indicate that the normal extremal controls can be expressed by the
Weierstrass elliptic function, while the abnormal extremal controls can only be
constant functions of time t.
