We consider the eigenfunctions of the Schrödinger operator with growing potential on the Euclidean space. To localize the eigenfunctions on the phase space, we construct a decomposition of the phase space into rectangles and show that each eigenfunction has some non-trivial mass concentrated near the corresponding energy shell. This is an ongoing joint project with Stefano Decio, Jaume De Dios Pont, and Svetlana Mayboroda.