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An uncertainty principle for fermions with generalized kinetic energy. (English) Zbl 0946.81521
Summary: We derive semiclassical upper bounds for the number of bound states and the sum of negative eigenvalues of the one-particle Hamiltonians \(h=f(-i\nabla)+V(x)\), acting on \(L^2({R}^n)\). These bounds are then used to derive a lower bound on the kinetic energy \(\sum^N_{j=1}\langle\psi,f(-i\nabla_j)\psi\rangle\) for an \(N\)-fermion wavefunction \(\psi\). We discuss two examples in more detail: \(f(0)=|p|\) and \(f(p)=\break (p^2+m^2)^{1/2}-m\), both in three dimensions.”.

MSC:
81V55 Molecular physics
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