The movie takes some license with the White Witch scene. She doesn't actually appear in the book, but in the movie, to drum the tension in the scene up, they have her appear in some spirit form. Here's the scene in question

https://www.youtube.com/watch?v=7IE4d0amYQ4

We know it's her because this is what [she says in the movie](http://www.narniaweb.com/features/Prince-Caspian-Movie-Script.pdf)

> *Peter pushes Caspian away and points his sword at the Witch.*
>
> **Peter:** Get away from him!
>
> *The White Witch falls back a little.*
>
> **White Witch:** Peter dear... I have missed you. Come, just one 
drop.

She's addressing Peter by name. Considering some 200 years have passed in Narnia, it's highly unlikely anyone else would recognize Peter solely by sight. Given that she wants a "drop of Adam's blood", it's not just some phantasm. The implication is she will be reincarnated if she gets it.