given a self-adjoint operator(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \mathcal L [y(x)]=-\lambda_{n} y(x) [/tex]

where the index 'n' can be any positive real number (continous spectrum) then my question is if

[tex] \int_{c}^{d}\int_{a}^{b}dn y_{n}(x)y_{m} (x)w(x)dx = 1 [/tex]

deduced from the fact that for continous n and m then the scalar product

[tex] <y_{n} |y_{m} > =\delta (n-m) [/tex] (Dirac delta --> continous Kronecker delta --> discrete case )

am i right ?? ... for the problem we have a continous set of eigenvalues [tex] \lambda _{n}=h(n) [/tex] where n >0 is any real and positive number

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# Continous spcetrum

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