(adsbygoogle = window.adsbygoogle || []).push({}); Can a self adjoint operator have a continous spectrum ??

If we have a self adjoint operator

[tex] Ly_{n} = \lambda _{n} [/tex]

can n take arbitrary real values (n >0 ) in the sense that the spectrum will be continous ?

and in that case, what is the orthonormality condition for eigenfunctions

[tex] <y_{n} |y_{m}>= \delta (n-m) [/tex]

where 'd' is dirac delta, as a generalization of discrete case of Kronecker delta. could someone put an example ? (since all the cases from QM i know the spectrum is discrete) thankx

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# Can a self adjoint operator have a continous spectrum ?

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