2010/04/30 by Leonor García-Gutierrez, Leonor Garcia-Gutierrez, Satoru Odake +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Eigenfunction #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Quantum no-deleting theorem #Quantum process #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.CA #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1143/ptp.124.1
published as Prog.Theor.Phys.124:1-26,2010 · 31 pages, 2 figures. Two typos (eq.(3.16), ref.[15]) corrected, several comments added. To appear in Progress of Theoretical Physics
arxiv created 2010/06/03 · openalex publication_date 2010/07/01 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Crum's theorem in one-dimensional quantum mechanics asserts the existence of an associated Hamiltonian system for any given Hamiltonian with the complete set of eigenvalues and eigenfunctions. The associated system is iso-spectral to the original one except for the lowest energy state, which is deleted. A modification due to Krein-Adler provides algebraic construction of a new complete Hamiltonian system by deleting a finite number of energy levels. Here we present a discrete version of the modification based on Crum's theorem for the ‘discrete’quantum mechanics developed by two of the present authors.