Derivations and biderivations of the n-th Schrödinger algebra

The n-th Schrödinger algebra schn:=sl2⋉hn is the semi-direct of the Lie algebra sl2 with the n-th Heisenberg Lie algebra hn. In this paper, all derivations and biderivations of the n-th Schrödinger algebra are determined. As applications, all linear commuting maps and commutative post-Lie algebra structures on schn are obtained.