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Results tagged with quantum-mechanics
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user 25999
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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Commutator with a square root
How to find the commutator $[a, \sqrt{a^\dagger a}]$? Here $a$ is a usual bosonic annihilation operator, and $[a, a^\dagger] = 1$.
The first thing I tried is
$$
[x,A] = [x, \sqrt{A}]\sqrt{A} + \sqrt{ …
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