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Application of the Method of Standard Comparison Problems to Perturbations of the Coulomb Field. The Discrete Spectrum

  • S. Yu. Slavyanov
Part of the Topics in Mathematical Physics book series (TOMP, volume 4)

Abstract

The present paper is devoted to obtaining asymptotic expansions for ε → 0 for the eigen-fiinctions Ψn(r) and eigenvalues En of Sturm-Liouville problems related to the radial Schrödinger equation
$$\begin{array}{l} \psi (r) + \left[ {2(E - V(r,\varepsilon )) - \frac{{l(l + 1)}}{{{r^2}}}} \right]\psi (r) = 0 \\ l = 0,1,2,...,r \in [0,\infty ) \\ \end{array}$$
(1)
where the potential V(r, ε) is composed of the Coulomb potential and a small perturbation
$$ V(r,\varepsilon ) = - \frac{1}{r} - \varepsilon \omega (\varepsilon r) $$
(2)
.

Keywords

Discrete Spectrum Airy Function Principal Quantum Number Unperturbed Problem Nonintegrable Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • S. Yu. Slavyanov

There are no affiliations available

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