In the story line of "Hamlet", do you think the apparition of his father the king is a real apparition, or is it part of Hamlet's delusion?

I just finished watching the 1948 film version of Hamlet, starring and directed by Sir Laurence Olivier. Over the years, I have ben involved in several productions of the play, in addition to having studied it in high school, and it rates as my favorite of all Shakespeare’s tragedies.
Do you think Hamlet is truly crazy, or is there a method to his madness, as Polonius says>