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)


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
$$\begin{array}{l} \psi (r) + \left[ {2(E - V(r,\varepsilon )) - \frac{{l(l + 1)}}{{{r^2}}}} \right]\psi (r) = 0 \\ l = 0,1,2,...,r \in [0,\infty ) \\ \end{array}$$
where the potential V(r, ε) is composed of the Coulomb potential and a small perturbation
$$ V(r,\varepsilon ) = - \frac{1}{r} - \varepsilon \omega (\varepsilon r) $$


Discrete Spectrum Airy Function Principal Quantum Number Unperturbed Problem Nonintegrable Singularity 
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Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • S. Yu. Slavyanov

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