I would define infatuation as love with obsession. We usually do not consider it as real as actual love, and it can be fleeting. It’s not hard to find quotes demonstrating the actual infatuation.
Romeo and Juliet fall in love very quickly. Is love at first sight real? That is a philosophical question, but I would definitely call it infatuation. Friar Lawrence’s comment to Romeo reminds us that just the day before he was pining for Rosaline.
Holy Saint Francis! What a change is here!
Is Rosaline, that thou didst love so dear,
So soon forsaken? Young men's love then lies
Not truly in their hearts, but in their eyes.
Jesu Maria! What a deal of brine(70)
Hath wash'd thy sallow cheeks for Rosaline! (Act II, Scene III)
For other examples of infatuation, we can go to Romeo and Juliet’s first meeting. Romeo sees her and asks who she is, his reaction?
O, she doth teach the torches to burn bright! (Act I, Scene 5)
As he goes on with that speech, you can tell he’s infatuated, and he has not even met the girl yet! He finishes up with ….
Did my heart love till now? Forswear it, sight!
For I ne'er saw true beauty till this night.(55) (Act I, Scene 5)
I’d say he’s infatuated!
Juliet seems to think about it a little more, but she still comes to the same conclusion.
My only love, sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me
That I must love a loathed enemy.(150) (Act I, Scene 5)
Juliet may be a little more cool headed than the fiery Romeo, but she clearly is infatuated too. She is already calling him her “only love” and she just met him too.
In the famous balcony scene, Romeo shows how much he has fallen for Juliet by comparing her to the sun and suggesting that the moon is jealous.
But soft! What light through yonder window breaks?
It is the East, and Juliet is the sun!
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief(5)
That thou her maid art far more fair than she.
Be not her maid, since she is envious. (Act II, Scene 2)
If you need more quotes, consider that even though the relationship develops it still shows signs of infatuation. The quick wedding, and Romeo’s reluctance to leave, shows he has not had his fill of the relationship.
It was the lark, the herald of the morn;
No nightingale. Look, love, what envious streaks
Do lace the severing clouds in yonder East.
Night's candles are burnt out, and jocund day
Stands tiptoe on the misty mountain tops.(10)
I must be gone and live, or stay and die. (Act III, Scene V)
There is also the fact that Romeo kills himself when he sees Juliet apparently dead, and Juliet kills herself when she sees what he’s done.
Yea, noise? Then I'll be brief. O happy dagger!
Snatches Romeo's dagger.
This is thy sheath; there rust, and let me die.(175) (Act V, Scene 3)
When you can’t live without someone, that’s infatuation.