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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16701 |
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Table of Contents:
- We show that the equations of motion of the rigid body about centre of mass in the Newtonian field with a quadratic potential are special reductions of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. We show that the corresponding matrix Schrödinger operators are maximally finite-gap (in the sense that for all sufficiently large energies all solutions of the corresponding Schrödinger equation are bounded) and describe their spectrum explicitly. The general $2\times 2$-matrix case of the dressing chain, providing also some exotic matrix versions of the harmonic oscillator, is discussed in more detail.