臺灣博碩士論文加值系統

量子混沌是近幾十年來研究的熱門學科，眾多判斷古典系統是否為混沌的方法並無法一一的套用在量子系統上，但「熵」是可以同時在古典與量子系統上計算得到的。若系統的熵與時間有關，則該系統極有可能是混沌，因此本文將挑選兩個量子系統計算其「訊息熵」，這兩個系統分別為(i)無限位能阱(ii)Gauss波包穿隧delta位壘，再針對其結果是否與時間有關進行探討。

Study of quantum chaos is a popular subject in recent decades.The rules of determining in classical system is chaotic could not apply in quantum systems, but the entropy is able to be calculated on both of classical and quantum systems. If the entropy of the system is dependent on time, it may be a chaotic system. We will choose two quantum systems to calculate their information entropy, and the two systems are (i) infinite quantum-well (ii) a Gaussian wave packet tunneling through a δ barrier.
We will discuss the results are time-dependent or time-independent.

1 前言.................................2
1.1 混沌...............................2
1.2 量子混沌的研究.....................6
2 由Gauss波包構成的量子系統............9
2.1 自由的Gauss波包....................9
2.2 Gauss波包穿隧δ位壘...............10
3 訊息熵的計算........................17
3.1 無限位能阱中的訊息熵..............17
3.2 Gauss 波包穿隧δ位壘之訊息熵......23
3.3 Gauss 波包穿隧δ位壘之高階修正項..30
4 結論與討論..........................37
參考書目..............................40

圖目錄
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