Lobachevsky平面内含杂质量子点的光谱
On the Spectrum of a Quantum Dot with Impurity in the Lobachevsky Plane
摘要：
考虑了一个在Lobachevsky平面内含有杂质的量子点模型。依赖于明确的公式的格林函数和克莱因$Q-$功能，已在以前的工作中，我们专注于数值分析的频谱。分析是复杂的事实，基本公式表示的球函数的一般特征指数。研究了曲率对本征值和本征函数的影响。此外，给出了曲率半径趋于无穷大（平坦情况极限）时特征值的渐近展开式。
英文摘要：
A model of a quantum dot with impurity in the Lobachevsky plane is considered. Relying on explicit formulae for the Green function and the Krein $Q-$function which have been derived in a previous work we focus on the numerical analysis of the spectrum. The analysis is complicated by the fact that the basic formulae are expressed in terms of spheroidal functions with general characteristic exponents. The effect of the curvature on eigenvalues and eigenfunctions is investigated. Moreover, there is given an asymptotic expansion of eigenvalues as the curvature radius tends to infinity (the flat case limit).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
