Limit-point / limit-circle classification of second-order differential operators arising in PT quantum mechanics

Büttner, Florian; Trunk, Carsten GND

We consider a second-order dierential equation −y′′+q(x)y(x) = y(x) with complex-valued potential q and eigenvalue parameter ∈ C. In PT quantum mechanics the potential has the form q(x) = −(ix)N+2 and is dened on a contour ⊂ C. Via a parametrization we obtain two dierential equations on [0;∞) and (−∞; 0]. With a WKB-analysis we classify this problem according to the limit-point/ limit-circle scheme.

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Büttner, Florian / Trunk, Carsten: Limit-point / limit-circle classification of second-order differential operators arising in PT quantum mechanics. Ilmenau 2016.

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