Hermitian operator eigen-stuff

[@1ashad1]

For Check your understanding:- 1) position op (PO) is hermitian. 2) The eigenfunction is a delta function positioned/centered at the eigenvalue x', and since x' can lie anywhere on the x-axis, the spectrum is continuous. 3) As said above, the eigenfunction is a delta function positioned/centered at the eigenvalue x'. 4) Not quite sure about this one! Can anyone help me with this?

[@Dekoherence-ii8pw]

19:00 "It SORT OF goes to zero". I'm thinking it might DEFINITELY GO TO ZERO if we use the Lebesgue Integral.

[@kaltoii]

Cool! Thank you for your clear explanation.

[@VincentStevenson]

How do you prove if a Hermitian operator has continuous or discrete spectrum? Or is something you just see?

[@puritybundi8204]

discrete spectrum the wavefunction is normalizable while for continuous it's not normalizable. Also, for discreet you can prove for reality of eigenvalues, then orthogonomality and completeness. While for continuous these properties fail

[@diegotapiasilva7349]

Should it not be delta(chi -x) ? on 22.26 mins?

[@osamaishtiak6135]

Nope the video is correct.

[@ifrazali3052]

​@@osamaishtiak6135 how?