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mixed spectra


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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
§1.18(viii) Mixed Spectra and Eigenfunction Expansions
It is to be noted that if any of the λ 𝝈 have degenerate sub-spaces, that is subspaces of orthogonal eigenfunctions with identical eigenvalues, that in the expansions below all such distinct eigenfunctions are to be included. … See §18.39 for discussion of Schrödinger equations and operators. … …
2: 18.39 Applications in the Physical Sciences
Brief mention of non-unit normalized solutions in the case of mixed spectra appear, but as these solutions are not OP’s details appear elsewhere, as referenced. … Namely for fixed l the infinite set labeled by p describe only the L 2 bound states for that single l , omitting the continuum briefly mentioned below, and which is the subject of Chapter 33, and so an unusual example of the mixed spectra of §1.18(viii). …
3: Bibliography S
  • B. W. Shore and D. H. Menzel (1968) Principles of Atomic Spectra. John Wiley & Sons Ltd., New York.
  • I. N. Sneddon (1966) Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.
  • I. I. Sobelman (1992) Atomic Spectra and Radiative Transitions. 2nd edition, Springer-Verlag, Berlin.