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How many numbers do you need?
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You need x, y, z for every particle.
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Right? So you need 3N arguments for Ψ.
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So Ψ is a function that
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when you tell it where all these positions are,
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it gives you a number. Now curiously enough,
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the number can be positive, it can be zero, it can be negative,
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it can even be complex, right,
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although we won't talk about cases where it's complex.
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The physicists will tell you about those,
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or physical chemists. Okay?
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And sometimes it can be as many as 4N+1 arguments.