A high-precision study of anharmonic-oscillator spectra
- Department of Physics and Nuclear Theory Center, Indiana University, Bloomington, Indiana 47405 (United States)
High-precision methods are developed to evaluate eigenvalues for all states {vert_bar}{ital m,N}{r_angle} of the x{sup 2m} anharmonic oscillators with {ital m} from 2 to 6, for all values of the anharmonicity parameter. There are three basic steps: rescaling to introduce a length scale natural to the problem; use of fifth-order JWKB to generate an accurate starting estimate of the rescaled energy; and shifted (resolvent-based) Lanczos algorithm to sharpen the initial JWKB estimate. JWKB itself gives 33-figure accuracy for {ital N} greater than 1500 (for m=2) to 3500 (for m=6). With the JWKB starting energy, the shifted Lanczos algorithm converges to 33 figures in 3 iterations or less for all states. These methods are used in a study of the systematics of anharmonic-oscillator spectra and of the physical effects of the rescaling transformation. {copyright} 1999 Academic Press, Inc.
- Research Organization:
- Indiana University
- DOE Contract Number:
- FG02-87ER40365
- OSTI ID:
- 324897
- Journal Information:
- Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 271; ISSN 0003-4916; ISSN APNYA6
- Country of Publication:
- United States
- Language:
- English
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