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Upper limit of the discrete hydrogen-like wave functions: Expansion in the inverse principal quantum number n−1 (1997)

Blaive, Bruno ; Cadilhac, Michel

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 38 (1997), S. 6061-6071

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: We have expanded the Schrödinger hydrogen-like wave functions ψnlm of the discrete spectrum, with respect to the inverse principal quantum number n−1, for fixed values of the quantum numbers l,m. The Laguerre polynomials Lnα(x/n) are expanded with respect to n−1 into a sum of Bessel functions multiplied by powers rk of the distance from the origin. The coefficients of the expansion are a family of polynomials sq,k(l) of the variable l, which can be computed with a recursion formula. The development, which converges rapidly, can be truncated after a few terms, even for low levels n. © 1997 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.532202

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