Perturbation of Spectra in Hilbert Space

accessory acting adjusted analytic annihilation Appendix apply associated assume basic belong bounded called Chapter Clearly commutes completely components condition connected consider consists continuous contracted contributions converge corresponding creation defined definition denoted depends derived described difference discussed disturbed eigenvalue eigenvector energy equation evidently existence expression fact factor field finite follows formula function gentle given hence Ho-representer holds identity implies integral integral operator interaction interval introduce inverse involved kernel limit multiple norm Note observe obtain operator H particle perturbation present problem projector prove referred relation renormalization representation represented require respect restricted result satisfy scattering single smooth solution space spectral spectral representation spectrum statement sufficiently tends theory transformation V₁₁ values vanishes variables vector verified w₁ wave Wick write written zero