The eigenfunctions of the curl operator are obtained by separation of variables in spherical coordinates, making use of the spin‐weighted spherical harmonics. It is shown that the eigenfunctions of the curl operator with vanishing divergence can be written in terms of a single scalar potential that satisfies the Helmholtz equation. It is also shown that these eigenfunctions give a complete basis for the divergenceless vector fields.

1.
Z.
Yoshida
,
J. Math. Phys.
33
,
1252
(
1992
).
2.
S.
Chandrasekhar
and
P. C.
Kendall
,
Astrophys. J.
126
,
457
(
1957
).
3.
P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 2.
4.
E. T.
Newman
and
R.
Penrose
,
J. Math. Phys.
7
,
863
(
1966
).
5.
J. N.
Goldberg
,
A. J.
Macfarlane
,
E. T.
Newman
,
F.
Rohrlich
, and
E. C. G.
Sudarshan
,
J. Math. Phys.
8
,
2155
(
1967
).
6.
R. Penrose and W. Rindler, Spinors and Space-time (Cambridge University, Cambridge, 1984), Vol. 1.
7.
T.
Dray
,
J. Math. Phys.
26
,
1030
(
1985
).
8.
H. E.
Moses
,
SIAM J. Appl. Math.
21
,
114
(
1971
).
9.
G. F.
Torres del Castillo
,
Rev. Mex. Fís.
38
,
19
(
1992
).
10.
G. F.
Torres del Castillo
,
Rev. Mex. Fís.
38
,
863
(
1992
).
11.
G. F.
Torres del Castillo
,
Rev. Mex. Fís.
37
,
147
(
1991
) (in Spanish ).
12.
Z.
Yoshida
and
Y.
Giga
,
Math. Z.
204
,
235
(
1990
).
13.
G. F.
Torres del Castillo
and
C.
Uribe Estrada
,
Rev. Mex. Fís.
38
,
162
(
1992
) (in Spanish ).
14.
G. F.
Torres del Castillo
and
J. E.
Rojas Marcial
,
Rev. Mex. Fís.
39
,
32
(
1993
).
This content is only available via PDF.
You do not currently have access to this content.