FEYNMAN PATH FORMULA FOR THE TIME FRACTIONAL SCHRODINGER EQUATION

被引：2
|
作者：
Emamirad, Hassan [1 ]
Rougirel, Arnaud [1 ]
机构：
[1] Univ Poitiers, Lab Math, Teleport 2,BP 179, F-86960 Chassneuil Du Poitou, France
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2020年 / 13卷 / 12期
关键词：
Feynman path formula; time fractional in the sense of Caputo; Mittag-Leffler function; Wright function;
D O I：
10.3934/dcdss.2020246
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we define E-alpha(t(alpha)A), where A is the generator of an uniformly bounded (C-0) semigroup and E-alpha(z) the Mittag-Leffler function. Since the mapping t bar right arrow E-alpha(t(alpha)A) has not the semigroup property, we cannot use the Trotter formula for representing the Feynman operator calculus. Thus for the Hamiltonian H-alpha = -h(alpha)2/2m Delta + V(x), we express E-alpha(t(alpha)H(alpha)) by subordination principle of the Feynman path integral and we retrieve the corresponding Green function.
引用
收藏
页码：3391 / 3400
页数：10
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