Archive of posts on Nov 13, 2025
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From Picard iteration to Feynman path integral
The Schrödinger equation is an ODE, so we can approach its solution through Picard iteration. This approach leads to a sum over walks on the graph formed by an orthonormal basis as vertices and the Hamiltonian matrix elements as edge weights. This sum is exactly the Feynman path integral if we choose the position basis and take the continuum limit.
- Categories: physics
- Tags: ode, quantum mechanics, graph theory, stochastic process, long paper