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Title: REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS

Abstract

Elementary treatrients of a single angular momentum having componerts J / sub k/ (k = 1, 2, 3) usually go as far as discussions of the spectra of these operators and the derivations of their standard, i.e., J/sup 2/, J/sub 3/- diagonal, representatives. On the other hand, the standard representatives of their eigenvectors are not usually obtained, leaving J/sub 3/ aside, for which the problem is trivial. ln fact, this part of the theory is most often dealt with only after a lengthy excursion into the theory of matrix representations. The representatives in question are obtained here by means of essentially elementary arguments. Once these representatives are known, the standard representative of the unitary operator U which generates the state vector of a system after it has undergone a rotation R from the state vector prior to the rotation is deduced; this representative conaprises just the familiar matrix representations of the rotation group. The relevance of harmonic oscillator theor to this problem is briefly considered. (auth)

Authors:
Publication Date:
Research Org.:
Australian National Univ., Canberra
Sponsoring Org.:
USDOE
OSTI Identifier:
4167540
NSA Number:
NSA-18-000920
Resource Type:
Journal Article
Journal Name:
American Journal of Physics (U.S.)
Additional Journal Information:
Journal Volume: Vol: 31; Other Information: Orig. Receipt Date: 31-DEC-64
Country of Publication:
Country unknown/Code not available
Language:
English
Subject:
PHYSICS; EIGENVECTORS; GROUP THEORY; MATHEMATICS; MATRICES; MOMENTUM; OSCILLATIONS; QUANTUM MECHANICS; ROTATION; SPECTRA; VECTORS

Citation Formats

Buchdahl, H A. REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS. Country unknown/Code not available: N. p., 1963. Web. doi:10.1119/1.1969135.
Buchdahl, H A. REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS. Country unknown/Code not available. https://doi.org/10.1119/1.1969135
Buchdahl, H A. 1963. "REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS". Country unknown/Code not available. https://doi.org/10.1119/1.1969135.
@article{osti_4167540,
title = {REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS},
author = {Buchdahl, H A},
abstractNote = {Elementary treatrients of a single angular momentum having componerts J / sub k/ (k = 1, 2, 3) usually go as far as discussions of the spectra of these operators and the derivations of their standard, i.e., J/sup 2/, J/sub 3/- diagonal, representatives. On the other hand, the standard representatives of their eigenvectors are not usually obtained, leaving J/sub 3/ aside, for which the problem is trivial. ln fact, this part of the theory is most often dealt with only after a lengthy excursion into the theory of matrix representations. The representatives in question are obtained here by means of essentially elementary arguments. Once these representatives are known, the standard representative of the unitary operator U which generates the state vector of a system after it has undergone a rotation R from the state vector prior to the rotation is deduced; this representative conaprises just the familiar matrix representations of the rotation group. The relevance of harmonic oscillator theor to this problem is briefly considered. (auth)},
doi = {10.1119/1.1969135},
url = {https://www.osti.gov/biblio/4167540}, journal = {American Journal of Physics (U.S.)},
number = ,
volume = Vol: 31,
place = {Country unknown/Code not available},
year = {1963},
month = {11}
}