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 ...

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Spin in magnetic field and eigenvalues

We have some arbitrary quantum state, lets say $$\vert\Psi\rangle=\alpha_{1}\vert\uparrow\rangle+\alpha_{2}\vert\downarrow\rangle= \begin{pmatrix} \alpha_{1} \\ \alpha_{2} \\ \end{pmatrix}$$. And ...