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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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de Broglie wavelength of electrons and holes
I think this article: https://en.wikipedia.org/wiki/Thermal_de_Broglie_wavelength, does a great job explaining why you'd need to know the de Broglie wavelength.
From a quick read, the basic reasoning …
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Why does the energy of an electron depend on the size of the well?
In the square well the energy states of the electron depend on the width of the square well. That means that by changing the physical shape of the confinement region (making it a parabolic well) or ma …