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Orthogonal polynomial expansion of the spectral density operator and the calculation of bound state energies and eigenfunctions

✍ Scribed by Wei Zhu; Youhong Huang; D.J. Kouri; Colston Chandler; David K. Hoffman

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 639 KB
Volume: 217
Category: Article
ISSN: 0009-2614
DOI: 10.1016/0009-2614(93)e1345-h

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✦ Synopsis

the spectral density operator (SDO), the projection operator that projects out of any Lz wavepacket the eigenstate( s) of H having energy E. If applied to an Lz wavepacket which overlaps the interaction, it yields either scattering-type (improper) eigenstates or proper bound eigenstates. For negative energies, the exact SD0 yields zero away from an eigenvalue, and yields the energy eigenstate (times a constant) when E equals an eigenvalue. The finite orthogonal polynomial expansion of the SDO, acting on an L* wavepacket, yields approximately zero for E not equal to an eigenvalue, and becomes nonzero in the neighborhood of an eigenvalue.

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