Generalization of Schrodinger equation to two-bodybound state : its application on Cooper pair and exciton

• Main Authors: Ming-Han Hsiao, 蕭銘翰
• Other Authors: Cheng-Hsuan Chen
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/22745277366726615295

博士 === 國立臺灣大學 === 物理研究所 === 99 === The investigation of optical spectrums among various materials has been a major task for physical research, mainly to deal with the complex interaction among electrons, the so-called exchange-correlation kernel, within some given solids or molecules. Both theoretically and numerically this is by all means a very challenging problem, which attracts many great minds into the regime, and many useful techniques and powerful tools have been developed for decades. In this work I propose a two-bound extension version of Schrodinger equation, as well as the Green function correspondingly. As a first attempt, this work aims to apply the method to some well-known two-body bound state, the Cooper pair in BCS theory and the exciton in BSE, where BSE in solid state society is in fact the very equation which triggers me in the first place to get into this way of thinking. The derivation of the method proposed is given, and the results and predictions are shown in the text. The method may require further study, and actually this is just a starting point. In the future, I wish to develop the method up to the quantum field regime, which means the second quantization scheme is needed which should be consistent with the equation of motion of Green function and in this sense, the quantum field theory could gain more physical interpretation and be generalized to some extent more than its usual plane-wave form. This is actually in line with the thought of so called Schrodinger field.