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Padé approximants to the evolution operator through the Lippmann Schwinger variational principle
Author(s) -
Calamante F.,
Grinberg H.
Publication year - 1995
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560540302
Subject(s) - operator (biology) , diagonal , harmonic oscillator , ladder operator , mathematics , unitary state , unitary operator , hermitian matrix , mathematical physics , shift operator , perturbation (astronomy) , connection (principal bundle) , mathematical analysis , quantum mechanics , physics , pure mathematics , compact operator , hilbert space , biochemistry , chemistry , geometry , repressor , computer science , transcription factor , political science , law , extension (predicate logic) , gene , programming language
Using the connection between the evolution operator and the stationary value of the Lippmann–Schwinger functional, approximations to this operator are obtained using diagonal Padé approximants. A harmonic oscillator with a non‐hermitean perturbation proportional to powers of the bosonic creation operator is considered and its evolution operator is evaluated. The poles of the spectral representation obtained by this method are compared to both: the ones of the usual perturbative expansion and those of the exact solution. Extensions to Hermitian Hamiltonians are discussed, involving the necessity of inverting more complex operators in the calculation of the Fourier transform. However, the approximation obtained by this procedure becomes exactly unitary. © 1995 John Wiley & Sons, Inc.