Спектр оператора Шрeдингера в накрытии эллиптического кольца

Никулин, Михаил Александрович; Nikulin, Mikhail Aleksandrovich

doi:10.55959/msu0579-9368-1-64-5-4

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Discussion and Further Developement1

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2023

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“…And in both cases, we found the asymptotic of energy levels as ε → 0 up to the second order. Our methods were successfully applied to find the asymptotic of energy levels in an elliptic ring, see [16].…”

Section: Discussion and Further Developementmentioning

confidence: 99%

Asymptotic behaviour of energy levels of a quantum free particle in an elliptic sector

Nikulin,

Popelensky,

Shafarevich

2023

Phys. Scr.

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We study quantum solution for a free particle in a domain bounded by an ellipse and arc(s) of confocal hyperbola(s). We found asymptotic behaviour of energy levels as focal distance tends to zero and show how it is related to the energy levels of limiting wedge billiard. Classical billiard system in the considered domains is integrable due to existence of an additional conserved quantity. There is a corresponding quantum counterpart, and we calculate its eigenvalues.

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Section: Discussion and Further Developementmentioning

confidence: 99%