  This is the continuation of a previous article, in which the Bjorken and
Voloshin sum rules were interpreted as statements of conservation of
probability and energy. Here the formalism is extended to higher moments of the
Hamiltonian operator. From the conservation of the second moment of the
Hamiltonian operator one can derive a sum rule which, in the small velocity
limit, reduces to the Bigi--Grozin--Shifman--Uraltsev--Vainshtein (BGSUV) sum
rule. On the other hand, the conservation of the third moment of the
Hamiltonian operator gives a new sum rule, which is related to the matrix
element of the heavy quark counterpart of the Darwin term in atomic physics.
The general case of the higher order moments is also discussed.
