An Uncertainty Principle for Fermions with Generalized Kinetic Energy

We derive semiclassical upper bounds for the number of bound states and the sum of negative eigenvalues of the one-particle Hamiltonians h = f ( ~ ) + V(x), acting on L2(N"). These bounds are then used N to derive a lower bound on the kinetic energy ~ ( q ~ , f ( i V y ) 0 ) for an j = l N-fermion wavefunction ~. We discuss two examples in more detail: f(P) = ]P[ and f(p) = (p2 + m2)1/2 _ m, both in three dimensions.