DOI: 10.1063/1.1746344. The Asymmetric Rotor. VI. Calculation of Higher Energy Levels by Means of the Correspondence Principle

The Asymmetric Rotor. VI. Calculation of Higher Energy Levels by Means of the Correspondence Principle

10.1063/1.1746344

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The rotational levels of the rigid asymmetric rotor can be calculated by means of the correspondence principle. It is shown that the quantum-number ratio K/J(J+1) is the complete elliptic integral of the third kind tabulated by Heuman in the case of the energy levels of a hypothetical rotor with reciprocal moments of inertia −1, κ, and +1. The parameter of the integral is the reduced-energy ratio E(κ)/J(J+1), and its modulus is a function of both the reduced-energy ratio and asymmetry parameter. A double inverse interpolation has been made by Heuman's table to give the energy ratio directly in terms of quantum-number ratio and asymmetry. Power series expansions have been developed around limiting cases and around each point in the table, so that formulas for interpolation and estimating errors are available.

Bibliography

King, G. W. (1947). The Asymmetric Rotor. VI. Calculation of Higher Energy Levels by Means of the Correspondence Principle. The Journal of Chemical Physics, 15(11), 820â830.

Authors 1

Gilbert W. King (first)

References 13 Referenced 44

{'key': '2024020812580169400_r1', 'first-page': '394', 'volume': '19', 'year': '1918', 'journal-title': 'Physik. Zeits.'} / Physik. Zeits. (1918)
{'key': '2024020812580169400_r2', 'first-page': '289', 'volume': '20', 'year': '1919', 'journal-title': 'Physik. Zeits.'} / Physik. Zeits. (1919)
10.1007/BF01397496 / Zeits. f. Physik (1926)
10.1073/pnas.12.10.602 / Proc. Nat. Acad. Sci. (1926)
10.1002/sapm1941201127 / J. Math. and Phys. (1941)
10.1007/BF01342264 / Zeits. f. Physik (1932)
10.1063/1.1723778 / J. Chem. Phys. (1943)
{'key': '2024020812580169400_r8'}
{'key': '2024020812580169400_r9'}
{'key': '2024020812580169400_r10'}
10.1080/14786440308636811 / Phil. Mag. (1910)
{'key': '2024020812580169400_r12'}
{'key': '2024020812580169400_r13'}

Dates

Type	When
Created	20 years, 7 months ago (Jan. 9, 2005, 6:56 a.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 7:59 a.m.)
Indexed	1 year, 6 months ago (Feb. 10, 2024, 12:26 a.m.)
Issued	77 years, 10 months ago (Nov. 1, 1947)
Published	77 years, 10 months ago (Nov. 1, 1947)
Published Print	77 years, 10 months ago (Nov. 1, 1947)

Funders 0

None

BibTeX

@article{King_1947, title={The Asymmetric Rotor. VI. Calculation of Higher Energy Levels by Means of the Correspondence Principle}, volume={15}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1746344}, DOI={10.1063/1.1746344}, number={11}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={King, Gilbert W.}, year={1947}, month=nov, pages={820–830} }

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