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In this paper, we study weight representations over the Schr{\"o}dinger Liealgebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that thealgebra $\mathfrak{s}_n$ can be realized by polynomial differential operators.Using this realization, we give a complete classification of irreducible weight$\mathfrak{s}_n$-modules with finite dimensional weight spaces for any $n$. Allsuch modules can be clearly characterized by the tensor product of$\mathfrak{so}_n$-modules, $\mathfrak{sl}_2$-modules and modules over the Weylalgebra.

Irreducible weight modules over the Schr{\"o}dinger Lie algebra in $(n+1)$ dimensional space-time