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題 名 | An Improved Semi-Classical Approximation Based on Heisenberg's Matrix Mechanics |
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作 者 | Li,Ching-teh; Klein,Abraham; | 書刊名 | Chinese Journal of Physics |
卷 期 | 39:6 2001.12[民90.12] |
頁 次 | 頁555-564 |
分類號 | 331.311 |
關鍵詞 | |
語 文 | 英文(English) |
英文摘要 | We have previously shown that the WKB and the Einstein-Brillouin-Keller (EBK) semi-classical quantization methods can be derived within a framework provided by Heisenberg matrix mechanics. Based on the relationship between quantum mechanical matrix elements and classical Fourier components, in a form emphasized in our earlier work, we suggest a modification of the semiclassical calculation that yields markedly improved values for the matrix elements of the elementary position and momentum operators, especially for low-lying states where the WKB values are poorest. The computational framework also provides quantum-mechanical sum rules for the energies that yield similarly improved values when evaluated with the new matrix elements. The scheme is illustrated by application to the quartic oscillator. |
本系統中英文摘要資訊取自各篇刊載內容。