Maurer-Cartan methods in perturbative quantum mechanics
arXiv:2401.17476
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 so that its cohomology becomes the space of solutions with a set 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.
11 pages