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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Distribution of eigenvalues in the presence of higher order turning points


Author: Anthony Leung
Journal: Trans. Amer. Math. Soc. 229 (1977), 111-135
MSC: Primary 34B25; Secondary 34E20
DOI: https://doi.org/10.1090/S0002-9947-1977-0447699-3
MathSciNet review: 0447699
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Abstract: This article is concerned with the eigenvalue problem $ u''(x) - {\lambda ^2}p(x)u(x) = 0,u(x) \in {L_2}( - \infty ,\infty )$, where $ p(x)$ is real, analytic and possesses zeroes of arbitrary orders. Under certain conditions on $ p(x)$, approximate formulas for the eigenvalues are found. The problem considered is of interest in the study of particle scattering and wave mechanics. The formula is analogous to the quantum rule of Bohr-Sommerfeld.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0447699-3
Keywords: Linear differential equations, boundary value problem, eigenvalues, turning points, connection formulas
Article copyright: © Copyright 1977 American Mathematical Society