- #1
Klaus_Hoffmann
- 86
- 1
Can a self adjoint operator have a continuous 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 continuous ?
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
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 continuous ?
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