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• W2029046828 abstract "Central potentials V(r) are considered that admit the polar representation V(r) = g(h(r)), where h(r) = sgn (q)r q , q is fixed, and g is the polar transformation function. This representation allows the Schrödinger eigenvalues generated by V to be approximated in terms of those generated by the pure polar potential h(r). In many cases a pair of powers {q 1 , q 2 } can be chosen so that the corresponding polar functions {g 1 , g 2 } have definite and opposite convexity. For such cases, the spectral approximations provide both upper and lower bounds for the entire discrete spectrum. The example V(r) = ar 2 + br 2 /(1 + cr 2 ) is considered in detail. PACS No. 03.65Ge" @default.
• W2029046828 created "2016-06-24" @default.
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• W2029046828 date "1998-01-01" @default.
• W2029046828 modified "2023-09-27" @default.
• W2029046828 title "Spectral approximation by the polar transformation" @default.
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• W2029046828 doi "https://doi.org/10.1139/p97-047" @default.
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