We have previously shown that the WKB and the Einstein-Brillouin-Keller (EBK) semiclassical 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 lowlying 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.
為了持續優化網站功能與使用者體驗,本網站將Cookies分析技術用於網站營運、分析和個人化服務之目的。
若您繼續瀏覽本網站,即表示您同意本網站使用Cookies。