Unitary Operator Formalism of the Eigenvalue Problems

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Abstract
Utilization of the parameters involved in the system under consideration leads to a unitary operator formalism for dealing with eigenvalue problems. The existence of a unitary linear operator which transfers a known function, being predetermined for a special choice of the parameter, to the general eigenfunction is demonstrated and its properties are discussed. The related hypervirial theorems for variational Hellmann—Feynman wavefunction are discussed. The scaling problem and virial theorem are treated in some detail by means of the unitary operator techniques.

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