# mixed spectra

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## 3 matching pages

##### 1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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###### §1.18(viii) Mixed Spectra and Eigenfunction Expansions

… ► It is to be noted that if any of the $\lambda \in \bm{\sigma}$ 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

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►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.
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►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). …