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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.

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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.

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A rigorous treatment of the Feynman-Kac formula is given in the chapter 3 of the book "Quantum Physics: A Functional Integral Point of View" by J. Glimm and A. Jaffe: http://www.springer.com/in/book/9780387964775

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