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 Hamiltoniansh=f(?i?)+V(x) acting onL ²(?ⁿ). These bounds are then used to derive a lower bound on the kinetic energy \(\sum\limits_{j = 1}^N {\left\langle {\psi ,f( - i\nabla _j )\psi } \right\rangle }\) for anN-fermion wavefunction ψ. We discuss two examples in more detail:f(p)=|p| andf(p)=(p ²+m ²)^1/2?m, both in three dimensions.