Bounds on variation of the spectrum and spectral subspaces of a few-body   Hamiltonian
  We overview the recent results on the shift of the spectrum and norm bounds for variation of spectral subspaces of a Hermitian operator under an additive Hermitian perturbation. Along with the known results, we present a new subspace variation bound for the generic off-diagonal subspace perturbation problem. We also demonstrate how some of the abstract results may work for few-body Hamiltonians. 
Sergio Albeverio, Alexander K. Motovilov
math-ph math.MP quant-ph