Spinning top in quadratic potential and matrix dressing chain

2025/04/23 by Adler, V. E., Veselov, A. P.
#37J35 #70H06 #81R12 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2504.16701

Abstract

We show that the equations of motion of the rigid body about a fixed point in the Newtonian field with a quadratic potential are special reduction of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. Some new explicit solutions of the corresponding matrix system and the spectral properties of the related Schrödinger operators are discussed.

Citations

• An overview of periodic elliptic operators
• Spectral estimates for Schrödinger operator with periodic matrix potentials on the real line
• Factorization of differential operators, quasideterminants, and nonabelian Toda field equations
• Integrability and non-integrability in Hamiltonian mechanics
• Integrals of nonlinear equations of evolution and solitary waves

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• Dirac-like Hamiltonians associated to Schrödinger factorizations
• Construction of solutions of analogs of the Schrodinger time equations corresponding to the Hamiltonian system H²⁺²⁺¹
• Eigenfunctions of spinless particles in a one-dimensional linear potential well
• A Spinning Particle in a Mobius Strip