Kac-Schwarz operators of type B, quantum spectral curves, and spin Hurwitz numbers

Given a tau-function $\tau(t)$ of the BKP hierarchy satisfying $\tau(0)=1$, we discuss relation between its BKP-affine coordinates on isotropic Sato Grassmannian and BKP-wave function. Using this result, formulate type Kac-Schwarz operators for in terms coordinates. As an example, compute affine spin single Hurwitz numbers with completed cycles, find pair $(P,Q)$ $[P,Q]=1$. By doing this, obtain quantum spectral curve numbers.