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

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    $\begingroup$ Wouldn't this be a better fit for Quantitative Finance? $\endgroup$
    – Steve S
    Commented Nov 18, 2014 at 21:31
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    $\begingroup$ I agree with Steve. The Black-Scholes is very related to quantitative financing, which is only one small portion of economics as a whole. $\endgroup$ Commented Nov 18, 2014 at 22:30
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    $\begingroup$ @SteveS I wonder if we might benefit from a meta discussion as to whether we should avoid poaching questions that can go on specific sub-discipline stacks? :-) $\endgroup$ Commented Nov 19, 2014 at 2:21
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    $\begingroup$ This question appears to be off-topic because pertains much more to quantitative finance than economics. $\endgroup$
    – daOnlyBG
    Commented Nov 19, 2014 at 9:13
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    $\begingroup$ @daOnlyBG that doesn't make it off-topic. It's a valid economics question. The fact that it could be on-topic at another site doesn't make it off-topic here at all. Whether it's answerable, and whether it's an appropriate expert question, is a different matter: but just being valid on more than one SE site is not a sufficient reason to close or to migrate. $\endgroup$
    – 410 gone
    Commented Nov 19, 2014 at 14:02

1 Answer 1


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.)

  • $\begingroup$ Yes, the Black-Scholes differential equation can be transformed into the heat equation by a change of variables. $\endgroup$
    – Geremia
    Commented Feb 5, 2018 at 21:37
  • $\begingroup$ Well, the Schrodinger equation is the complex analysis equivalent of the heat equation so the relationship seems legit. $\endgroup$ Commented Mar 27, 2018 at 18:26

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