Friday, 13 October 2017

quantum mechanics - What's the relation between path integral and Dyson series?


If one solves the Schrodinger equation



$$i\hbar\partial_tU(t,0) = H U(t,0)$$



for time evolution operator $U(t,0)$, one can get the following Dyson series




$$U(t,0) = \sum_n(\dfrac{-i}{\hbar})^n\int_0^t dt_1 \int_0^{t_1}dt_2 \cdots \int_0^{t_{n-1}} d t_n H(t_1)H(t_2) \cdots H(t_n) .$$



So my question is: is there any relationship between every term in the Dyson series and the possible path in Feynman's path integral method for quantum mechanics?




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