Abstract
A recently-formulated residue-squaring method for perturbation problems is subjected to an exacting test in its application to the problem of diagonalising the Hamiltonian of the nonlinear oscillator with quartic anharmonicity. Unlike other methods, this new iterative diagonalisation method enables several eigenvalues to be calculated simultaneously with little more labour than for a single eigenvalue. Values obtained for the four lowest even-parity levels of the anharmonic oscillator from just two or three iterations are shown to agree well with earlier accurate calculations. An approximate analytical formula for the energy levels is also presented.
Similar content being viewed by others
References
Bender C M and Wu T T 1969Phys. Rev. 184 1231
Biswas S Net al 1971Phys. Rev. D4 3617
Biswas S Net al 1973J. Math. Phys. 14 1190
Graffi S, Grecchi V and Simon B 1970Phys. Lett. B32 631
Graffi S and Grecchi V 1975Lett. Nuovo Cimento 12 425
Hioe F T and Montroll E W 1975J. Math. Phys. 16 1945
Loeffel Jet al. 1969Phys. Lett. B30 656
Mathews P M and Eswaran K 1972Lett. Nuovo Cimento 5 15
Mathews P M 1975Pramāna 4 53
Simon B 1970Ann. Phys. 58 76
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mathews, P.M., Govindarajan, T.R. Residue-squaring diagonalisation method and the anharmonic oscillator. Pramana - J. Phys. 8, 363–370 (1977). https://doi.org/10.1007/BF02847806
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02847806