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chern
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We all know that quantum theory is based on the commutation relation and superposition principle. The trouble haunting me long time is that how to "get" the famous commutation relation? Could anybody give me an explanation?
atyy said:The commutation relation is a fundamental postulate and cannot be derived.
The commutation relation between q and p is given by [q, p] = qp - pq, where q and p are operators in quantum mechanics.
The commutation relation is derived from the Heisenberg uncertainty principle, which states that the product of the uncertainties in position and momentum must be greater than or equal to the reduced Planck's constant, h-bar.
The commutation relation is important because it helps us understand the behavior of quantum mechanical systems. It also plays a crucial role in the formulation of the Heisenberg uncertainty principle and the principles of quantum mechanics.
The commutation relation has physical significance because it tells us that position and momentum cannot both be known with arbitrary precision in quantum mechanics. It also helps us determine the allowed energy levels and the dynamics of a quantum system.
Yes, the commutation relation can be generalized to any two operators in quantum mechanics. The commutator of two operators A and B is defined as [A, B] = AB - BA, and it plays a similar role in determining the properties and behavior of quantum systems.