Derivatives of Phase Shifts and Binding Energies by Use of Variational Principles

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Abstract
The Kohn‐Hulthén variational principle for the phase shifts, as well as the Rayleigh‐Ritz principle for the binding energies, are used to determine the derivatives of δl = δ(V, E, l, m, ℏ) and E = E(V, l, m, ℏ) with respect to the listed parameters. A similar treatment utilizing Hamilton's variational principle leads to the corresponding classical results. The relation between the quantum mechanical and the classical expressions is examined. In particular, it is found that the quantum‐mechanical binding energy corresponds to a certain path average of the classical energy. Some applications of resulting formulas are briefly reviewed. This work is an extension of ideas originated by Fock and Demkov.