nZ 碎形量子空間

Abstract

在本次研究中，我們用了三個主要的工具來探討nZ非線性系統的現象，此 參種工具包括了Catalan number, Schwarzian derivative與 generating operator。在本論文中，我們推導了一些通式(general formula)從而描述並了解nZ非線性系統，其在"Quantum Space"中規則 (regular)與不規則(irregular)的現象。最後吾入深信透過此次研究，對 於量子力學統計現象與算符代數，將有一番新的認識。 Three kinds of machinery have been used to investigate the nonlinear system nZ, namely Catalan number analysis, Schwarzian derivative and generating operator. We have also obtained some general formula to describe the regular and irregular nonlinear phenomena in "quantum space". Finally, this implication can allow us to understand the statistical problems in quantum mechanics by this operator algebra.