What does the scene on the castle's battlements in Shakespeare's Hamlet, reveal about Prince Hamlet's state of mind?

At the beginning of William Shakespeare's play,
Hamlet, Horatio comes to Hamlet to tell him that Old Hamlet's ghost
has appeared on the battlements. Hamlet assures Horatio that he will join him there
later, to see the spirit himself.

In Act One, scene four,
Hamlet joins Horatio and Marcellus on the battlements at midnight. When Hamlet sees the
Ghost, he reacts in several ways.

First, Hamlet approaches
the Ghost, determined to speak to it.

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HAMLET:

...Be
thou a spirit of health or goblin damn'd,

Bring with thee
airs from heaven or blasts from hell,

Be thy intents wicked
or charitable,    (45)

Thou comest in such a questionable
shape

That I will speak to thee. I'll call thee
Hamlet,

King, father, royal Dane. O, answer
me!

Hamlet wants to know why
the Ghost, looking so like his father, is walking the
earth.

When the Ghost wants Hamlet to follow, Horatio and
Marcellus try to dissuade him, but Hamlet curiously moves to follow the spirit, still
not certain that it is his father's ghost.

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HAMLET:

It
will not speak; then will I follow
it.

HORATIO:

Do
not, my
lord!

HAMLET:

Why,
what should be the fear?(70)

I do not set my life at a
pin's fee;

And for my soul, what can it do to
that,

Being a thing immortal as
itself?

It waves me forth again. I'll follow
it.

At this point, Horatio
and Marcellus, fearful that the Ghost may be evil, sent from hell to trick Hamlet, try
to physically prevent Hamlet from following. Hamlet defies them with his bravery, and
furiously threatens the men—committed for his father's sake to hear what the Ghost has
to say:

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HAMLET:

My
fate cries out,(90)

And makes each petty artery in this
body

As hardy as the Nemean lion's*
nerve.

[Ghost
beckons.]

Still am I call'd. Unhand me,
gentlemen.

By heaven, I'll make a ghost of him that lets
me.

I say, away! Go on. I'll follow thee.  
(95)

From the beginning of
this scene until the end, Hamlet welcomes the possibility that the Ghost may be his
father. He is curious. He is committed. And ultimately, he bravely, even defiantly,
chooses to follow the Ghost to hear what it has to say. Hamlet explains to his
companions that his mind is not only committed to his purpose, but the very arteries in
his body hum with the need to follow the specter. Hamlet is firm of purpose and clear of
mind.

Hamlet's state of mind in scene four is clear, and he
is determined to speak with the Ghost.

*Nemean
lion's nerve: "As hardy as the nerve of the lion killed by
Hercules"