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Maurer-Cartan methods in perturbative quantum mechanics (2401.17476v1)
Published 30 Jan 2024 in math-ph and 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.
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