翻訳と辞書 Words near each other ・ Born reciprocity ・ Born Reckless ・ Born Reckless (1930 film) ・ Born Reckless (1937 film) ・ Born Reckless (1958 film) ・ Born Red ・ Born Rich ・ Born Rich (film) ・ Born Rich (TV series) ・ Born rigidity ・ Born Romantic ・ Born Ruffians ・ Born rule ・ Born Sandy Devotional ・ Born secret ・ Born series ・ Born Sinner ・ Born Slippy ・ Born Slippy .NUXX ・ Born Standing Up ・ Born Stunna ・ Born Suspect ・ Born That Way ・ Born That Way (film) ・ Born This Way ・ Born This Way (album) ・ Born This Way (Glee) ・ Born This Way (song) ・ Born This Way Ball ・ Born This Way Foundation Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Born series ： ウィキペディア英語版 Born series The Born series is the expansion of different scattering quantities in quantum scattering theory in the powers of the interaction potential $V$ (more precisely in powers of $G\_0\; V,$ where $G\_0$ is the free particle Green's operator). It is closely related to Born approximation, which is the first order term of the Born series. The series can formally be understood as power series introducing the coupling constant by substitution $V\; \backslash to\; \backslash lambda\; V$. The speed of convergence and radius of convergence of the Born series are related to eigenvalues of the operator $G\_0\; V$. In general the first few terms of the Born series are good approximation to the expanded quantity for "weak" interaction $V$ and large collision energy. ==Born series for scattering states== The Born series for the scattering states reads :$|\backslash psi\backslash rangle\; =\; |\backslash phi\; \backslash rangle\; +\; G\_0(E)\; V\; |\backslash phi\backslash rangle\; +\; (V)^2\; |\backslash phi\backslash rangle\; +\; (V)^3\; |\backslash phi\backslash rangle\; +\; \backslash dots$ It can be derived by iterating the Lippmann–Schwinger equation :$|\backslash psi\backslash rangle\; =\; |\backslash phi\; \backslash rangle\; +\; G\_0(E)\; V\; |\backslash psi\backslash rangle.$ Note that the Green's operator $G\_0$ for free partice can be retarded/advanced or standing wave operator for retarded $|\backslash psi^\backslash rangle$ advanced $|\backslash psi^\backslash rangle$ or standing wave scattering states $|\backslash psi^\backslash rangle$. The first iteration is obtained by replacing the full scattering solution $|\backslash psi\backslash rangle$ with free particle wave function $|\backslash phi\backslash rangle$ on the right hand side of the Lippmann-Schwinger equation and it gives the first Born approximation. The second iteration substitutes the first Born approximation in the right hand side and the result is called the second Born approximation. In general the n-th Born approximation takes n-terms of the series into account. The second Born approximation is sometimes used, when the first Born approximation vanishes, but the higher terms are rarely used. The Born series can formally be summed as geometric series with the common ratio equal to the operator $G\_0\; V$, giving the formal solution to Lippmann-Schwinger equation in the form :$|\backslash psi\backslash rangle\; =\; (-\; G\_0(E)\; V)^\; |\backslash phi\; \backslash rangle\; =\; (-\; VG\_0(E)\; V)^\; V\; |\backslash phi\; \backslash rangle\; .$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Born series」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.