Nj. Kylstra, ON THE UNIQUENESS OF THE ATOMIC BRILLOUIN STATE EXPANSION, Journal of physics. B, Atomic molecular and optical physics, 27(24), 1994, pp. 5815-5823
We show that the expansion coefficients appearing in the general expre
ssion for a coupled atomic wavefunction satisfying Brillouin's theorem
must satisfy a matrix equation. In some circumstances this matrix equ
ation is underdetermined, so that the coefficients of the Brillouin ex
pansion are not unique. This is illustrated by considering some exampl
es.