Generating and computing quantum periods in exact WKB

Periods of rational integrals appear in quantum mechanics through asymptotic expansions of traces computed with the semiclassical symbol calculus. In particular, a novel formal series expansion for the trace of the Dirac delta of the quantization of a polynomial Hamiltonian is developed. Reducing these integrals modulo total derivatives results in a novel formula for normal forms of the integrals. In the case of one degree of freedom, the two-dimensional residue formula relates the rational integrals to the quantum actions in the exact WKB formalism.