# Hydrogen-Like Continuum Eigenstates

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The positive-energy continuum states of a hydrogen-like system are described by the eigenfunctions with corresponding eigenvalues , (). are the same spherical harmonics that occur for the bound states. In atomic units , the radial equation can be written . The solutions with the appropriate analytic and boundary conditions have the form . These functions are deltafunction-normalized, such that . They have the same functional forms (apart from normalization constants) as the discrete eigenfunctions under the substitution .

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Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

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Reference: H. A. Bethe and E. E. Salpeter, *Quantum Mechanics of One- and Two-Electron Atoms*, New York: Academic Press, 1957, pp. 21–25.

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