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Quantum Simulation
Modification of Crum's Theorem for `Discrete' Quantum Mechanics
arXiv
Authors: Leonor Garcia-Gutierrez, Satoru Odake, Ryu Sasaki
Year
2010
Paper ID
9077
Status
Preprint
Abstract Read
~2 min
Abstract Words
92
Citations
N/A
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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- 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...
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