Non-weight modules over the super Schrödinger algebra

We construct a family of non-weight modules which are free \(U(\frak{h})\) $$U(\mathfrak{h}\mathfrak{)}$$ -modules of rank 2 over the N = 1 super Schrödinger algebra in (1+1)-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free \(U(\frak{h})\) $$U(\mathfrak{h}\mathfrak{)}$$ -modules of rank 2 over \(\frak{osp}(1\mid 2)\) $$\mathfrak{o}\mathfrak{s}\mathfrak{p}\mathfrak{(}\mathfrak{1}\mid \mathfrak{2}\mathfrak{)}$$ are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.