Description
Starting from a spectral curve $S$ (a plane curve with some structure), Topological Recursion defines a sequence of differential forms, called $\omega_{g,n}(S)$. From this sequence, one can define a formal series $\ln\psi(\hbar,S,x) = \sum_{g,n} \frac{1}{n!}\hbar^{2g-2+n} \int_\infty^x \dots \int_\infty^x \omega_{g,n}(S)$, called the "wave function" (the TR wave function).
An important claim is that this wave function is annihilated by a differential operator with rational coefficients (and formal series of $\hbar$). In fact to make the claim complete, one has to extend it to transseries. The differential operator is called the "quantum curve" or the "quantization of the spectral curve".
