Communications in Mathematical Physics

, Volume 90, Issue 4, pp 511–520 | Cite as

An uncertainty principle for fermions with generalized kinetic energy

  • Ingrid Daubechies
Article

Abstract

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 onL2(ℝn). 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)=(p2+m2)1/2m, both in three dimensions.

Keywords

Neural Network Statistical Physic Kinetic Energy Complex System Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Ingrid Daubechies
    • 1
  1. 1.Physics DepartmentPrinceton UniversityPrincetonUSA

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