## Distribution of eigenvalues in the presence of higher order turning points

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- by Anthony Leung
- Trans. Amer. Math. Soc.
**229**(1977), 111-135 - DOI: https://doi.org/10.1090/S0002-9947-1977-0447699-3
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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.## References

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## Bibliographic Information

- © Copyright 1977 American Mathematical Society
- 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