Schrödinger operator on Wiener Amalgam spaces in the full range

Using the technique of Gabor analysis, an equivalent characterization is established for the boundedness $e^{i\mathrm{\Delta }}:W_m^{p,q}\to W^{p,q}$, where $0<p_i,q_i\le \mathrm{\infty }$ and $m$ is a $v$-moderate weight. The sharp exponents for the boundedness is also characterized in the case of power weight.