Schr\"{o}dinger operator on Wiener Amalgam spaces in the full range

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