Characteristic Functions of Quantum Trees

• Main Authors: Hui-Chen Huang, 黃惠禎
• Other Authors: Chun-Kong Law
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/45159217248911735567

碩士 === 國立中山大學 === 應用數學系研究所 === 101 === The characteristic function is a function on ℝ where zeros are exactly the eigenvalues of a quantum graph. We shall give a recursive formula which helps to build up the characteristic function of complicated quantum trees. In the case when the potential Q = 0, there is also a modified characteristic function which can have a direct formula for complicated quantum trees. We shall use the above two methods to show that there are two distinct quantum graphs having the same set of eigenvalues. In other words, they are isospectral quantum graphs. Many other examples of quantum graphs and their modified characteristic functions will also be given. The theoretical part of this thesis follow from the papers [3, 6].