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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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The Infinite Well
If the following list of functions defined on $x \in [0,L] \,$
$$\phi_n(x) \equiv \sqrt{\frac{2}{L}}\sin\left(\frac{n\pi}{L}x\right)$$ where $n$ is positive integer and the functions are zero at the b …