On Eigenfunctions of the Laplacian for Hecke Triangle Groups
On Eigenfunctions of the Laplacian for Hecke Triangle Groups
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关于赫克三角群拉普拉斯算子的本征函数
DOI：
10.1007/978-1-4612-1544-8_11
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发表时间：
1999
影响因子：
1.2
通讯作者：
D. Hejhal
中科院分区：
文献类型：
--
作者：
D. Hejhal
由于它们与薛定谔方程的密切联系，在负弯曲黎曼流形上拉普拉斯算子的平方可积本征函数的精确计算，特别是在高能极限下，应该成为量子混沌中的一个主要兴趣话题，这并不奇怪。毕竟，确定这样的本征函数就相当于考察给定黎曼流形R上的单个量子力学“粒子”--考虑到由于R的曲率为负而在R上盛行的经典混沌，这一追求具有一定的重要性。[1]
Because of their intimate connection with Schrodinger’s equation, it is not too surprising that the accurate calculation of square-integrable eigenfunctions of the Laplacian on negatively curved Riemannian manifolds, particularly in the high-energy limit, should have emerged as a topic of major interest within quantum chaos. The determination of such eigenfunctions is, after all, tantamount to examining individual quantum-mechanical “particles” on the given Riemannian manifold R — a pursuit of some importance given the classical chaos which prevails on R due to R’s curvature being negative.1