Abstract
A computationally facile super convergent perturbation theory for the energies and wavefunctions of the bound states of one-dimensional anharmonic oscillators is suggested. The proposed approach uses a Kolmogorov repartitioning of the Hamiltonian with perturbative order. The unperturbed and perturbed parts of the Hamiltonian are defined in terms of projections in Hilbert space, which allows for zero-order wavefunctions that are linear combinations of basic functions. The method is demonstrated on quartic anharmonic oscillators using a basis of generalized coherent states and, in contrast to usual perturbation theories, converges absolutely. Moreover, the method is shown to converge for excited states, and it is shown that the rate of convergence does not deteriorate appreciably with excitation.
Recommended Citation
G. S. Tschumper and M. R. Hoffmann, "Superconvergent Perturbation Theory for an Anharmonic Oscillator," Journal of Mathematical Chemistry, vol. 31, no. 1, pp. 105 - 120, Springer, Dec 2002.
The definitive version is available at https://doi.org/10.1023/A:1015438514814
Department(s)
Chemistry
Keywords and Phrases
Perturbation theory; Quantum mechanical oscillators; Superconvergence; Time-independent Schrödinger equation
International Standard Serial Number (ISSN)
0259-9791
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Springer, All rights reserved.
Publication Date
01 Dec 2002
Comments
National Science Foundation, Grant CHE-9975429