邊界位能在WKB上的影響

The effect of the side wall potential on the WKB approximation

李柄諭(Ping-Yu Li)

指導教授 ： 陳義裕

國立臺灣大學/理學院/物理學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201601724

摘要

物理學家一直在尋找計算束縛態能量的方法。從WKB 近似找到的量子化條件就是其中一種簡單又容易理解的方法。可是，在最原始的理論中仍有一些不足的地方。在這篇論文中, 我們將探討WKB 的適用情形並嘗試尋找高階修正項。另外，我們也將從量子化的物理意義下手，並計算在” 軟量子化” 條件不適用的情形下的束縛態能量。

關鍵字

束縛態能量 ； 量子化 ； 高階修正項

並列摘要

Physicists have been looking for ways to derive the bound state energies of different potentials. One of these methods is the quantization condition derived by WKB approximation, which easy to comprehend and imagine. However, there are still some defects in this theory. In this thesis, we’d checked the applicability of WKB under different conditions and tried to find out higher correction terms for quantization conditions. Besides, we'd calculated the bound state energies of some potentials that ”soft” turning point quantization condition isn’t applicable by starting from the meaning of quantization condition.

並列關鍵字

bound state energy ； higher correction terms ； quantization

參考文獻

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[4] N. Fromann and P. O. Fromann, Phase-Integral Method : Allowing Nearlying Transition Points, vol. 40. Springer Tracts in Natural Philosophy, 1995.