I'm doing some reading in Zettili's quantum mechanics book and came across this passage:
Now the thing I'm left dumbfounded on is why it can be considered normalizable? I tried finding some explanation in the book but that didn't yield anything other than some vague verbal argument for it. Now I tried just plugging the wave packet into the normalization condition and got some nasty looking integral expression that I'm not sure what to do with.
Maybe this is something trivial but as I'm trying to learn this on my own I'd really like to leave nothing unclear in my understanding so if someone could tell me why defining the wave function like this makes it normalizable that would be appreciated.