DOI: 10.1063/1.432266. Semiclassical eigenvalues for nonseparable systems: Nonperturbative solution of the Hamilton–Jacobi equation in action-angle variables

Semiclassical eigenvalues for nonseparable systems: Nonperturbative solution of the Hamilton–Jacobi equation in action-angle variables

10.1063/1.432266

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

It is shown how the Hamilton–Jacobi equation for a multidimensional nonseparable system can be efficiently solved directly in action-angle variables. This allows one to construct the total (classical) Hamiltonian as a function of the ’’good’’ action-angle variables which are the complete set of constants of the motion of the system; requiring the action variables to be integers then provides the semiclassical eigenvalues. Numerical results are presented for a two-dimensional potential well, and one sees that the semiclassical eigenvalues are in good agreement with the exact quantum mechanical values even for the case of large nonseparable coupling.

Bibliography

Chapman, S., Garrett, B. C., & Miller, W. H. (1976). Semiclassical eigenvalues for nonseparable systems: Nonperturbative solution of the HamiltonâJacobi equation in action-angle variables. The Journal of Chemical Physics, 64(2), 502â509.

Authors 3

Sally Chapman (first)
Bruce C. Garrett (additional)
William H. Miller (additional)

References 24 Referenced 166

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{'key': '2024020913443367100_r2', 'first-page': '69', 'volume': '25', 'year': '1974', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1974)
{'key': '2024020913443367100_r2a', 'first-page': '77', 'volume': '30', 'year': '1975', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1975)
{'key': '2024020913443367100_r3'}
{'key': '2024020913443367100_r4', 'first-page': '82', 'volume': '19', 'year': '1917', 'journal-title': 'Verh. Dtsch. Phys. Ges.'} / Verh. Dtsch. Phys. Ges. (1917)
{'key': '2024020913443367100_r5'}
10.1016/0003-4916(58)90032-0 / Ann. Phys. (N.Y.) (1958)
10.1016/0003-4916(60)90061-0 / Ann. Phys. (N.Y.) (1960)
{'key': '2024020913443367100_r7'}
10.1063/1.1665596 / J. Math. Phys. (1971)
10.1063/1.1678259 / J. Chem. Phys. (1972)
10.1088/0022-3700/6/9/002 / J. Phys. B (1973)
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{'key': '2024020913443367100_r13'}
{'key': '2024020913443367100_r14'}
{'key': '2024020913443367100_r15'}
{'key': '2024020913443367100_r16'}
{'key': '2024020913443367100_r17'}
{'key': '2024020913443367100_r18', 'first-page': '155', 'volume': '24', 'year': '1973', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1973)
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Dates

Type	When
Created	22 years, 6 months ago (Feb. 27, 2003, 5:10 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 9:31 a.m.)
Indexed	1 month, 3 weeks ago (July 2, 2025, 3:27 p.m.)
Issued	49 years, 7 months ago (Jan. 15, 1976)
Published	49 years, 7 months ago (Jan. 15, 1976)
Published Print	49 years, 7 months ago (Jan. 15, 1976)

Funders 0

None

BibTeX

@article{Chapman_1976, title={Semiclassical eigenvalues for nonseparable systems: Nonperturbative solution of the Hamilton–Jacobi equation in action-angle variables}, volume={64}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.432266}, DOI={10.1063/1.432266}, number={2}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Chapman, Sally and Garrett, Bruce C. and Miller, William H.}, year={1976}, month=jan, pages={502–509} }

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