  We consider the quadratic form of a general deterministic matrix on the
eigenvectors of an $N\times N$ Wigner matrix and prove that it has Gaussian
fluctuation for each bulk eigenvector in the large $N$ limit. The proof is a
combination of the energy method for the Dyson Brownian motion inspired by
[Marcinek, Yau 2020] and our recent multi-resolvent local laws [Cipolloni,
Erd\H{o}s, Schr\"oder 2020].
