Can an operator in quantum act upon any wave function that is not possible wave function, which is not square integrable, like delta function or momentum functi

yes right, but I got this dout when I saw this line in H C Verma book. see eq 6.2

here

see this

okay. thanks

welcome dear.

then delta function? and momentum eigen function?

we operate on them, but they are not square integrable?

no we can not operate that bcoz they are not eigen fxn

Delta function is not a valid wave function.

a operator can act on any function but it won't give any useful information. You can perform measurements and gather information about the system when it will be a acceptable wave function.

this must mean that we can not operate any operator on delta function?

This mean that delta function must not be eigen function of any wave function. and momentum eigen function also

dear dirac delta is a kind of potential

Wave fxn associated with it is another type

which is of course follows all condition of wf

okay. and similar is the case with momentum eigen function?

yes exactly

dear what is ur confusion

dirac delta is potential?

its a kind of potential not a wave fxn. wave fxn have property of wave...... . dirac delta is a type of potential my dear. not a wave fxn.

while dirac delta behave like infinite potential at x=0. it's not a wavy nature. so it's a potential not a wf.

here

operator has been operated upon a function which is not square integrable.

dear it is square integrable see my next comment

okay