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Relative states and Hidden Variables in Quantum Mechanics

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I ONLY NEED HELP WITH NUMBER ONE. It looks really long but the beginning is just a set up to the question. Skip to 'Your job' to see the question. I don't understand this stuff at all so if you could guide me through this step by step it would be appreciated. Explanations are important.

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Solution Summary

The relative states and hidden variables in quantum mechanics are determined. The importance are explained.

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