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- W2021923674 abstract "In studying various quantum-billiard configurations, R. L. Liboff (J. Math. Phys.35 (1994) 2218), was led to investigate the vanishing of f(ν)=j 2ν,1 - j ν2 , where j μk is the kth positive zero of the Bessel function J μ (x). Here we show that the even more general function f α (ν)=c αν,k - c ν,k+l is increasing and vanishes once (and only once) in 0<ν<∞, provided α≥π/2 and [Formula: see text], k, l=1,2,3,…. As usual, c μn is the nth positive zero of the cylinder function C μ (x)=J μ (x) cos θ - Y μ (x) sin θ. Specialized to Liboff's case, f(ν), this yields not only the existence of a zero of f(ν) but also its uniqueness." @default.
- W2021923674 created "2016-06-24" @default.
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- W2021923674 date "2003-10-01" @default.
- W2021923674 modified "2023-09-27" @default.
- W2021923674 title "BESSEL FUNCTIONS IN A QUANTUM-BILLIARD CONFIGURATION PROBLEM" @default.
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- W2021923674 doi "https://doi.org/10.1142/s0219530503000223" @default.
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