DOI: 10.1063/1.1747553. The Separation of the Rotational Coordinates from the <i>N</i>-Particle Schroedinger Equation

The Separation of the Rotational Coordinates from the N-Particle Schroedinger Equation

10.1063/1.1747553

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

By group theoretical arguments, it can be shown that a wave function, ψμL, for a system of N particles corresponding to a total angular momentum quantum number, L, and a quantum number, μ, referring to the z component of angular momentum may be written as a sum of terms: ψμL=Σs DL(R)μs*χsL.The DL(R)μs are the representation coefficients for the Lth irreducible representation of the three-dimensional rotation group, and are functions of the three coordinates specifying the orientation of the system of particles in space. The χμL are functions of the 3N−6 coordinates specifying the relative configuration of the N-particle system. The set of coupled differential equations for the functions, χμL, is obtained explicitly. The special case of the three-particle system is discussed in detail. The present treatment is more directly usable than the previous discussions since the basic equations do not involve implicit relationships between the variables.

Bibliography

Curtiss, C. F., Hirschfelder, J. O., & Adler, F. T. (1950). The Separation of the Rotational Coordinates from the N-Particle Schroedinger Equation. The Journal of Chemical Physics, 18(12), 1638â1642.

Authors 3

C. F. Curtiss (first)
J. O. Hirschfelder (additional)
F. T. Adler (additional)

References 4 Referenced 126

10.1073/pnas.21.2.113 / Proc. Nat. Acad. Sci. (1935)
{'key': '2024020813541440500_r2'}
{'key': '2024020813541440500_r3'}
10.1103/PhysRev.37.556 / Phys. Rev. (1931)

Dates

Type	When
Created	20 years, 7 months ago (Jan. 9, 2005, 7:19 a.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 8:54 a.m.)
Indexed	3 months, 4 weeks ago (May 3, 2025, 4:24 p.m.)
Issued	74 years, 9 months ago (Dec. 1, 1950)
Published	74 years, 9 months ago (Dec. 1, 1950)
Published Print	74 years, 9 months ago (Dec. 1, 1950)

Funders 0

None

BibTeX

@article{Curtiss_1950, title={The Separation of the Rotational Coordinates from the N-Particle Schroedinger Equation}, volume={18}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1747553}, DOI={10.1063/1.1747553}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Curtiss, C. F. and Hirschfelder, J. O. and Adler, F. T.}, year={1950}, month=dec, pages={1638–1642} }

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