REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS

Journal Article · Fri Nov 01 04:00:00 EST 1963 · American Journal of Physics (U.S.)

DOI:https://doi.org/10.1119/1.1969135· OSTI ID:4167540

Buchdahl, H A

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)

• Research Organization: Australian National Univ., Canberra
• Sponsoring Organization: USDOE
• NSA Number: NSA-18-000920
• OSTI ID: 4167540
• Journal Information: American Journal of Physics (U.S.), Journal Name: American Journal of Physics (U.S.) Vol. Vol: 31; ISSN AJPIA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

EIGENVECTORS
GROUP THEORY
MATHEMATICS
MATRICES
MOMENTUM
OSCILLATIONS
PHYSICS
QUANTUM MECHANICS
ROTATION
SPECTRA
VECTORS