Usefulness of hypervirial theorems in dealing with many problems in quantum chemistry and quantum mechanics is shown. Combined with the variation principle they become a tool in obtaining eigenvalues and eigenfunctions. Two parts: study of the hypervirial theorems when the range of the hypervirial operator is contained by the domain of the Hamiltonian operator; study of the form the hypervirial theorems adopt when the domain of the Hamiltonian operator does not contain the range of the hypervirial operator.
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