  This paper builds up two equivalence theorems for different kinds of optimal
control problems of internally controlled Schr\"{o}dinger equations. The first
one concerns with the equivalence of the minimal norm and the minimal time
control problems. (The minimal time control problems are also called the first
type of optimal time control problems.) The targets of the aforementioned two
kinds of problems are the origin of the state space. The second one deals with
the equivalence of three optimal control problems which are optimal target
control problems, optimal norm control problems and the second type of optimal
time control problems. These two theorems were estabilished for heat equations
in [18] and [17] respectively.
