I'm studying quantum mechanics and my professor has not made a full discussion on vectors with continuous index: the textbook that I follow is Cohen.
However he introduced some notions and expressions such as the following.
You can treat vectors with infinite rules as long as the scalar product with a finite vector is finite. $$ | E , \delta E \rangle = \frac{1}{\sqrt{\delta E}} \int_{E}^{E + \delta E} dE' |E' \rangle$$
I found something on the textbook, but I am not very satisfied, nor do I seem to have understood correctly.
Can anyone tell me where to find a treatment not too deep and mathematics but let me at least a superficial comprehension or introduce me to the subject.
Thank you so much.