Geodesic
Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 279-298 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe the spectral series of the Schrödinger operator $H=-(h^2/2) \Delta+V(x)+\alpha\delta(x-x_0)$, $\alpha\in\mathbb R$, with a delta potential on the real line and on the three- and two-dimensional standard spheres in the semiclassical limit as $h\to0$. We consider a smooth potential $V(x)$ such that $\lim_{|x|\to\infty}V(x)=+\infty$ 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.
Keywords: semiclassical spectrum, Schrödinger operator, delta potential, Lagrangian manifold, Maslov canonical operator. 
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     author = {T. A. Filatova and A. I. Shafarevich},
     title = {Semiclassical spectral series of {the~Schr\"odinger} operator with a~delta~potential on a~straight line and on a~sphere},
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T. A. Filatova; A. I. Shafarevich. Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 279-298. http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a7/

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