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Quantum Physics
Title: Bootstrapping the Kronig-Penney Model
(Submitted on 20 Sep 2022 (v1), last revised 29 Nov 2022 (this version, v2))
Abstract: Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schr\"odinger equation with periodic potentials, paying particular attention to the Kronig-Penney model of a particle in a one-dimensional lattice. With an appropriate choice of operator basis involving position and momenta, we find that the bootstrap approach efficiently computes the band gaps of the energy spectrum but has trouble effectively constraining the minimum energy. We show how applying more complex constraints involving higher powers of momenta can potentially remedy such a problem. We also propose an approach for analytically constructing the dispersion relation associated with the Bloch momentum of the system.
Submission history
From: Arpan Bhattacharyya [view email][v1] Tue, 20 Sep 2022 18:00:04 GMT (206kb,D)
[v2] Tue, 29 Nov 2022 13:25:38 GMT (206kb,D)
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