Year: 2025
Type: article
Abstract: Determining the solvability of a given quantum mechanical system is generally challenging. We discuss that the numerical bootstrap method can help us to solve this question in 1D quantum mechanics. We show that the bootstrap method can derive exact energy eigenvalues in systems with shape invariance, which is a sufficient condition for solvability and which many solvable systems satisfy. The information of the annihilation operators is also obtained naturally, and thus the bootstrap method tells us why the system is solvable. We numerically demonstrate this explicitly for shape-invariant potentials: harmonic oscillators, Morse potentials, Rosen–Morse potentials, and hyperbolic Scarf potentials. Therefore, the numerical bootstrap method can determine the solvability of a given unknown system if it satisfies shape invariance.
DOI: 10.1093/ptep/ptaf139
Authors: Yu Aikawa, Takeshi Morita
Institution: Shizuoka University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $979
OpenAlex ID: W4414874644