On the magneto-roton gap and the Laughlin state stability

It is argued that the Girvin, MacDonald and Platzman (GMP) evaluation of the magneto-roton spectrum, in spite of probably being a sensible estimate of the excitation spectrum around the real ground state, is not implying the variational stability of the Laughlin state. The suplementary corrections needed to produce a variational calculation around the Laughlin state at 1/3 value of the filling factor are evaluated approximately. The results indicate, within the considered approximation, the existence of lower lying states for a range of wavevector values.