gene-therapy
发表于 2025-3-23 10:13:52
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联想记忆
发表于 2025-3-23 16:43:54
Statement of Main Resultssemi-classical asymptotic formula called Birkhoff’s formula is proved from the standpoint of oscillatory integrals. In this chapter, these results as well as others are explained. Proofs will be given in subsequent chapters.
并入
发表于 2025-3-23 18:48:07
Feynman Path Integral and Schrödinger Equationtain the second term of the semi-classical asymptotic and prove that it satisfies the second transport equation. Our discussion of this is different from the usual method originated by Birkhoff (Bull Am Math Soc 39:681–700 (1933) ). Our method enables us to obtain the bound of the remainder term.
羊齿
发表于 2025-3-24 00:59:03
Path Integrals and Oscillatory Integralsegral techniques and is given a definite value under some conditions. We give an example of a sufficient condition for that in Sect. .. Furthermore, in such a case the stationary phase method, which is given by Theorem . in Sect. ., gives the value of the oscillatory integral asymptotically as ..
小鹿
发表于 2025-3-24 02:57:01
Path Integrals and Oscillatory Integralse factor . oscillates rapidly and as a consequence there occurs a large scale of cancellation. Such an integral is commonly treated by oscillatory integral techniques and is given a definite value under some conditions. We give an example of a sufficient condition for that in Sect. .. Furthermore, i
chalice
发表于 2025-3-24 06:46:21
Statement of Main Resultsies Assumption . and if the time interval is short, because it is an oscillatory integral that satisfies Assumption .. Furthermore, the time slicing approximation of Feynman path integrals converges to a limit as .. The limit turns out to be the fundamental solution of the Schrödinger equation. The
大沟
发表于 2025-3-24 12:49:17
Feynman Path Integral and Schrödinger Equationthe Schrödinger equation. The main tool is the .-boundedness theorem proof of which is left to Chap. . in Part II. By the way we shall prove that the main term of the semi-classical asymptotic of the fundamental solution of the Schrödinger equation satisfies the transport equations. At the end we ob
Isolate
发表于 2025-3-24 15:55:12
Stationary Phase Method for Oscillatory Integrals over a Space of Large Dimensionm is given, which is independent of the dimension. This theorem enables us to discuss the time slicing approximation of Feynman path integrals when the dimension of the space goes to .. This was the central tool of our discussions in Sect. 5.4 of Chap. ..
mediocrity
发表于 2025-3-24 21:21:14
0921-3767 y the time slicing method, the method Feynman himself used, This book proves that Feynman‘s original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and it
培养
发表于 2025-3-24 23:46:38
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