  The paper generalizes a result of Behrend-Fantechi and Baranovsky-Ginzburg to
the 1-shifted cotangent bundle $T^*X[1]$ of a smooth scheme $X$ over the field
of complex numbers. We show how one can obtain twisted cotangent bundles as
derived intersections of Lagrangians in $T^*X[1]$, moreover and we show that
the derived intersection of the quantized Lagrangians coincide with the
canonical quantization of the twisted cotangent bundles.
