环形鼓和量子环的光谱：微扰和非微扰结果
Spectroscopy of annular drums and quantum rings: perturbative and nonperturbative results
摘要：
通过将环形区域共形映射到单连通区域，得到了任意形状量子环（环形鼓）的态（能量和波函数）的系统近似。本文推广了文献\cite{Amore09}的一般结果，得到了任意形状量子环谱的一个解析公式：对于圆环和Robnik环，这个公式是非常简单和精确的。我们还得到了不同量子环的基态的精确变分界。最后，我们扩展共形配置方法的\cite{Amore08,Amore09}的类问题在这里考虑和计算精确的数值解大量的状态（$\approx 2000$）。
英文摘要：
We obtain systematic approximations to the states (energies and wave functions) of quantum rings (annular drums) of arbitrary shape by conformally mapping the annular domain to a simply connected domain. Extending the general results of Ref.\cite{Amore09} we obtain an analytical formula for the spectrum of quantum ring of arbirtrary shape: for the cases of a circular annulus and of a Robnik ring considered here this formula is remarkably simple and precise. We also obtain precise variational bounds for the ground state of different quantum rings. Finally we extend the Conformal Collocation Method of \cite{Amore08,Amore09} to the class of problems considered here and calculate precise numerical solutions for a large number of states ($\approx 2000$).
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