I am examining Berry's original 1984 paper of geometrical phases. I am having trouble understanding a portion of it, however (which is attached as a photo). In particular, equation (6) appears to have a bra-ket expression which includes the bra- complex conjugate of a state, <n(R)|, along with a ket |∇n(R)>. My question is, how is the resulting expression (the integral over space? of the product of these functions) another vector (as it must be since it is included in a line integral)?
41.5 KB Views: 353