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arXiv · 1004.0289

Modification of Crum's Theorem for `Discrete' Quantum Mechanics

Leonor Garcia-Gutierrez·Satoru Odake·Ryu Sasaki
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Abstract

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 the Crum's theorem for the `discrete' quantum mechanics developed by two of the present authors.

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Leonor Garcia-Gutierrez, Satoru Odake, Ryu Sasaki. 2010-06-03. Modification of Crum's Theorem for `Discrete' Quantum Mechanics. https://doi.org/10.1143/ptp.124.1

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