2019/08/20 by Primitivo B. Acosta-Humánez, Acosta-Humánez, Primitivo B., David Blázquez-Sanz +3
Mathematics · Physics and Astronomy · #34M15 #81Q35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1908.07666
openalex publication_date 2019/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present an algebraic study concerning the general second\norder linear differential equation with polynomial coefficients. By means of\nKovacic's algorithm and asymptotic iteration method we find a degree\nindependent algebraic description of the spectral set: the subset, in the\nparameter space, of Liouiville integrable differential equations. For each\nfixed degree, we prove that the spectral set is a countable union of non\naccumulating algebraic varieties. This algebraic description of the spectral\nset allow us to bound the number of eigenvalues for algebraically\nquasi-solvable potentials in the Schr "odinger equation.\n