  The power spectrum estimated from a galaxy redshift survey is the real
spectrum convolved with a window function, so when estimating the power on very
large scales (for small k), it is important that this window function be as
narrow as possible. A method that achieves this is presented. The optimal
estimate of P(k) is found to be the Fourier transform of the number density
fluctuations (n/nbar - 1) weighted by a function psi_0, and the optimal psi_0
is found to be the ground-state solution of the Schoedinger equation, with the
inverse selection function as the potential. This quantum mechanics analogy
occurs basically because we want the weight function to be narrow both in
Fourier space (to give a narrow window) and in real space (to minimize the
variance from shot noise). An optimal method for averaging the estimates at
different k-vectors is also presented, generalizing the standard procedure of
averaging over shells in k-space. Finally, a discrete version of the method is
presented, dividing space into ``fuzzy pixels", which has the advantage of
being able to handle redshift distortions in a straightforward way.
