I would like to have a reference with more in deep explanation of Feynman-Kac than in Evan's ‎An Introduction to Stochastic Differential Equations and, if possible, example of solution for equations like Schrödinger and others.



Reference for Feynman-Kac
Please see p.282 of the following ref, it does not call it Feynman-Kac Formula but the whole section 5 is discussing it. It formalized the diffusion using a tensor field over a manifold which is the most general and in-depth treatment from stochastic equation perspective that I know of.



> 
> Ikeda, Nobuyuki, and Shinzo Watanabe. Stochastic differential
>  equations and diffusion processes. Vol. 24. Elsevier, 2014.
> 
> 
> 


that is also where I learnt the material from. 


