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A practical solution to the “unknown normalization” problem
Author(s) -
Macías A.,
Martín F.,
Riera A.,
Yáañez M.
Publication year - 1988
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.560330404
Subject(s) - normalization (sociology) , wave function , autoionization , eigenvalues and eigenvectors , discretization , photoionization , simple (philosophy) , physics , quantum mechanics , statistical physics , mathematics , mathematical analysis , ionization , ion , philosophy , epistemology , sociology , anthropology
We analyze the theoretical basis of a procedure to determine an unknown normalization factor in discretized wave functions, which we have successfully used in a series of calculations of resonance widths for atomic and molecular systems. By reducing this determination to that of a suitable interpolation function for the energy eigenvalues, the problem is easily solved when atomic basis sets are chosen according to simple rules. Illustrations of our procedure are presented for atomic, molecular, and model systems; renormalized wave functions are compared with the exact ones for these model systems. The resulting method of renormalized continuum wave functions has a wide range of application in the study of long‐lived quasibound states (predissociation, autoionization, photoionization, unimolecular reactions, etc.).