Maurer-Cartan methods in perturbative quantum mechanics
Mathematical Physics
2024-02-01 v1 math.MP
Abstract
We reformulate the time-independent Schr\"odinger 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.
Cite
@article{arxiv.2401.17476,
title = {Maurer-Cartan methods in perturbative quantum mechanics},
author = {Andrey Losev and Tim Sulimov},
journal= {arXiv preprint arXiv:2401.17476},
year = {2024}
}
Comments
11 pages