臺灣博碩士論文加值系統

　　本論文係應用資訊理論中的最大熵程序，以探討簡單量子系統其獨立於時間的薛丁格方程式與資訊熵極值化的問題。我們發現連續資訊熵為一相對的概念，其本質為待測系統與參考系統之間的資訊熵差，所以其值有正有負。而且，資訊熵中的Ｓp和Ｓy不僅能反應出系統在位置及動量座標的行為，似乎也與位能和動能有極密切的關係。在簡諧振盪子和氫原子的問題中，我們以正規化和“位能對等定理”作為限制條件，可求得系統基態的波函數，再利用激發態與基態的正交性以及其節點性質的不同，可得到各系統各能階在徑向的波函數。

　　This is an analysis of the relationships between the time-independent Schrodinger equation and the information entropy maximization. We first compute entropies of various states of the three simple quantum systems, namely, the box-particle, the harmonic oscillator, and the hydrogen atom for re-examination and then find the nature of continuous entropy is a relative concept. We use potential equivalent theorem as a constraint, and through the maximum-entropy procedure we obtain the ground state Schrodinger equation of the systems. It is also found that there exists a variational procedure involving maximizing entropy for obtaining all solutions of the excited states once one solution is known. In the light of information theory, the ensemble concept in statistical thermodynamics is helpful to understand microscopic quantum systems and many quantum mechanical concepts.