Abstract
We describe the spectral series of the Schrödinger operator H = −(h2/2)Δ + V(x) + αδ(x−x0), α ∈ ℝ, with a delta potential on the real line and on the three- and two-dimensional standard spheres in the semiclassical limit as h → 0. We consider a smooth potential V(x) such that lim|x|→∞V(x)=+∞ in the first case and V(x) = 0 in the last two cases. In the semiclassical limit in each case, we describe the classical trajectories corresponding to the quantum problem with a delta potential.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 164, No. 2, pp. 279–298, August, 2010.
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Filatova, T.A., Shafarevich, A.I. Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere. Theor Math Phys 164, 1064–1080 (2010). https://doi.org/10.1007/s11232-010-0085-4
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DOI: https://doi.org/10.1007/s11232-010-0085-4