A general property of the quantum mechanical Hamiltonians for constrained systems

Whereas model constraints (e.g., frozen bonds, rigidified atomic groups, etc.) are often resorted to for the calculation of the potential energy surfaces of polyatomic molecules, the derivation of exact expressions for the corresponding kinetic energy operators is a rather new topic. Indeed, the dimensions of the configuration spaces being altered, the differential operators should be modified accordingly, but not the multiplicative operators. In addition, the physical condition J = 0 (where J is the total angular momentum vector) which, from a mathematical viewpoint, is a set of three constraints, also is often considered. The particular question raised is: in the derivation of the kinetic energy operator, is the order in which we apply the model constraints on the one hand and the dynamic constraints J = 0 on the other hand, immaterial? The answer is yes