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Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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Why can't I just think the spin as rotating?

(1) First argument An ordinary object that is spinning on an axis has an angular momentum which is determined by how the mass of the object is distributed about the axis, and how fast the object is s …
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How do I correctly interpret $\rho = \psi_1^* \psi_2$?

I'm not sure what a "probability density for transition" is - is it a probability density or a transition amplitude? I think you mean transition amplitude. Are you sure that $\rho = \psi_1^* \psi_2$ …
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