2021-07-29T18:42:03Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000117432021-07-05T00:36:40Z1169:1170Modification of Crum's Theorem for 'Discrete' Quantum MechanicsGarcia-Gutierrez, Leonor35999Odake, Satoru36000Sasaki, Ryu36001Crum'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.ArticlePROGRESS OF THEORETICAL PHYSICS. 124(1):1-26 (2010)journal articlePROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE2010-06application/pdfPROGRESS OF THEORETICAL PHYSICS11241260033-068XAA00791455https://soar-ir.repo.nii.ac.jp/record/11743/files/Modification_Crums_Theorem_Discrete_Quantum_Mechanics.pdfeng10.1143/PTP.124.1http://dx.doi.org/10.1143/PTP.124.1