The relation between the Black-Scholes model and quantum mechanics As an active participant on the Physics Stack Exchange I have, on several separate occasions, run into some vague remarks about the 'intimate relation' between the famous Black-Scholes model in economics and the Schrödinger equation that appears in quantum mechanics. In particular, people mention that path integrals (a certain technique that is very useful in quantum mechanical calculations) find many applications in economic settings. 

I'd love if someone could make this connection clearer by 


Explicitly (i.e. in equations) showing how the Schrödinger equation and the Black-Scholes equation are related
Discussing the use of path integrals in economics
I have more often heard of how the Black-Scholes equation is just the heat equation. You can find that information here. I haven't heard of a relationship between Black-Scholes and quantum mechanics before, but this post on the Physics stack exchange seems to have the details you're looking for. (Maybe you've seen this post before.)