In the last few years, the study of the continuous Anderson model has know a various developments thanks to both the regularity structure theory and the paracontolled approach. In this lecture, we aim to construct the Anderson-Hermite operator in dimension 1 and 2, that is the perturbation of Hermite operator by a spatial white noise potential. This construction is based on a quadratic form approach. After defining appropriate functional spaces, it is easy to define the 1d Anderson-Hermite operator, up to a random constant shift, as a lower-bounded, self-adjoint operator with compact resolvent. In 2d, the direct approach to define the quadratic form fails and one has to renormalize some quantity. We use an exponential transform adapted to the Hermite operator to exhibit the quantity to renormalize. I will present a construction of the Wick renormalization of the Anderson-Hermite operator and show it defines, up to a random constant shift, a lower-bounded, self-adjoint operator with compact resolvent.