WKB-Approximations and spectral asymptotics in one problem of singular perturbation theory
Copyright policy )WKB-Approximations and spectral asymptotics in one problem of singular perturbation theory
An \(O(\varepsilon^{3/2})\) approximation to the eigenvalues of the Sturm-Liouville problem \[ i \varepsilon y''(z)+(z^{2}-\lambda)y(z)=0, \;\varepsilon >0, \quad y(-1)=y(1)=0, \] is obtained. The result improves previous authors' results obtained in [Dokl. Math. 63, No. 3, 306--309 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 378, No. 1, 18--21 (2001; Zbl 1048.34141)].
- Lomonosov Moscow State University Russian Federation
Sturm-Liouville theory, asymptotic distribution of eigenvalues, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, nonselfadjoint Sturm-Liouville problem, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, WKB approximation, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, singular perturbation
Sturm-Liouville theory, asymptotic distribution of eigenvalues, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, nonselfadjoint Sturm-Liouville problem, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, WKB approximation, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, singular perturbation
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