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- W2006750218 abstract "Planck's constant h is a fundamental physical parameter that establishes the scale of quantum phenomena. Bound-state energy eigenvalues for several well-known systems (e.g., harmonic oscillators, Morse oscillators, and square-well potentials) are formally analytic functions of h in the neighborhood of h=0, and any ``physical'' state can be reached in principle by analytic continuation. This paper explores the possibility of developing power series in h for atomic and molecular energies, with analytic continuation to access physical states. For this purpose it is necessary to modify Coulomb interactions at short range to keep the potential bounded below. As a result the h expansions appear naturally as Rayleigh-Schrodinger perturbation series in anharmonicity about collective harmonic-oscillator states. Physical eigenvalues emerge in the strong-coupling limit, and Pad'e approximants seem to be analytical tools well suited for entering this regime. Some basic implementation details are presented for application to the modified hydrogen atom, the two-electron isoelectronic atomic sequence, and many-electron atoms." @default.
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- W2006750218 date "1991-04-01" @default.
- W2006750218 modified "2023-09-27" @default.
- W2006750218 title "Planck’s-constant expansions for bound states" @default.
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- W2006750218 doi "https://doi.org/10.1103/physreva.43.3317" @default.
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