Maurer–Cartan methods in perturbative quantum mechanics

Abstract

We reformulate the time-independent Schrödinger equation as a Maurer–Cartan equation on the superspace of eigensystems of the former equation. We then twist the differential such that its cohomology becomes the space of solutions with a fixed energy. A perturbation of the Hamiltonian corresponds to a deformation of the twisted differential, leading to a simple recursive relation for the eigenvalue and eigenfunction corrections.