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 Schrodinger 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 Schrodinger equation and the Black-Scholes equation are related

Discussing the use of path integrals in economics