Self-consistent wave function for magnetic polarons in thet-Jmodel

We derive a wave function for a single hole in the t-J model that is an approximate solution to the Schrödinger equation to all orders in the number of excited spin waves in the quasiparticle, for arbitrary values of t/J. The self-consistent Green-function equation used by Schmitt-Rink, Varma, and Ruckenstein and Kane, Lee, and Read arises as a consistency condition for the existence of a solution to the Schrödinger equation. The approximation provides a wave function for the strong-polaron problem due to electron-phonon coupling as well. The wave function predicts the same dipolar variation of the average staggered spin deviation at large distances, at the band minimum, as does the semiclassical wave function of Shraiman and Siggia, but the quasiparticle state is not orthogonal to the bare-hole state (${\mathit{z}}_{\mathit{k}}$≠0).