The ground state energy of the Schrodinger-Newton equation

We use the variational form of the stationary Schrodinger-Newton equations to find a lower bound for the ground state energy. The bound on the energy is incompatible with the value proposed by Kumar and Soni (Phys. Lett. A 271 (2000) 157) but consistent with the numerical values in the literature. To obtain the bound, we prove an identity which also shows that the eigenvalues of the Schrodinger-Newton equations are all negative. (C) 2001 Elsevier Science B.V. All rights reserved.