Phase conventions for angular momentum eigenfunctions

Ajoy Kumar Ghatak, S. Lokanathan

K. Tamvakis

D. Sourias, A. D. Jannussis, A. Streclas

In this paper we study the Wigner operators of angular momentum in the phase space, which are obtained from the well-known operators of angular momentum by virtue of Wigner representation. In the sequel we construct the Lie algebra of these operators, as well as the corresponding Lie group, and we examine two representations of this group. We find also the eigenfunction and the eigenvalues of these operators.

G. S. Japaridze, Anzor Khelashvili, K. Sh. Turashvili

Eigenfunctions and eigenvalues of the operator of the square of the angular momentum are studied. It is shown that neither from the requirement for the eigenfunctions be normalizable nor from the commutation relations it is possible to prove that the eigenvalues spectrum is a set of only integer numbers (in units $\hbar=1$). We present regular, normalizable eigenfunctions with the non-integer eigenvalues thus demonstrating that a non-integer angular momentum is admissible from the theoretical viewpoint.

Takeo Miura

The eigenfunctions and eigenvalues of orbital angular momentum operator on noncommutative lattice for a circle poset by theta-quantization are constructed, and it is demonstrated that they are equivalent to those of the conventional quantum mechanics.