Could it be that Hamlet was schizophrenic?

As we have seen in classes, in the movie, and of course in the book itself, Hamlet is a very complex play, as well as, some other plays written by Shakespeare. But Hamlet particularly has a more complex story and of course a more interesting character (Hamlet himself.)

To be honest I have problems making deep interpretations of the play, but I must say that I found really interesting the mental processes of The Prince of Denmark because as the play develops, he, I would say, goes in a spiral of madness that captures everybody in the play making them going crazy as he is. At first in act 1 secne 5 with the “apparition” of his father’s ghost, Hamlet was alone when he saw it. In that occasion the ghost of his father demands to be avenged by Hamlet because he says that Claudius poisoned him and killed him.  Taking into consideration that specific scene, and the fact that Hamlet was alone during that dialogue, I started thinking that probably that whole dialogue occurred in Hamlet’s mind. If that’s the case then probably Hamlet was a schizophrenic because as I found out, people that suffers from this mental disorder may hear voices in his head, may have visual hallucinations, may have problems separating fictions from reality, among other symptoms that Hamlet in a way showed during the play.
At the same time throughout the play, Hamlet acts to be mad, but I thinks that he does it as a way of hiding that he’s not mentally healthy. Even though the information that Hamlet received from his father’s ghost was true and correct, probably he got it from another part and he imagined as his dead father gave it.Simultaneously Hamlet gets paranoiac arguing that everybody is doing wrong and wants to harm him. If we pay attention to those aspects we can see another symptom of schizophrenia that is the fear of imagine another people plotting against them.

Moreover I found an essay (Findaly A. 1997) that analyzes the same topic, and the author uses an excerpt of the play in which Hamlet talks about his own madness:

What I have done

That might your nature, honour, and exception

Roughly awake, I here proclaim was madness.

Was't Hamlet wrong'd Laertes? Never Hamlet.

If Hamlet from himself be ta'en away,

And when he's not himself does wrong Laertes,

Then Hamlet does it not, Hamlet denies it.

Who does it then? His madness. If't be so,

Hamlet is of the faction that is wrong'd;

His madness is poor Hamlet's enemy.

(V. ii. 226-35)

Hamlet refers to his madness as a `sore distraction' with which he is currently afflicted (V. ii. 225), so his self-analysis is not a retrospective one except in the narrowest sense. He speaks both inside and outside his malady, as he had done earlier, making use of syntactic modification to explain and control his mental state. (Finlay A. 1997 )

To conclude I would say that Hamlet knew he wasn't mentally healthy and for that reason he acted as a mad men trying to avenge his father without thinking in the consequences of his acts. But we all know how everything ended and the deaths that occurred by those acts.
I would like to know what do you think about this, and if you have another hypotheses. Feel free to comment.

References: 

National Institute of Mental Health (n.d) What Is Schizophrenia? retrieved from: http://www.nimh.nih.gov/health/topics/schizophrenia/index.shtml

Findlay A. (1997) HAMLET: A DOCUMENT IN MADNESS  2007 Gale, Cengage Learning