Thursday 27 August 2020

quantum mechanics - How is quantization related to commutation?



How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence non-quantization, but I don't understand the intuition behind the fact that commutativity of operators should imply any kind of quantization.


In a theory involving `quantized' quantities, such as quantum mechanics, why does commutation of operators (observables) suddenly become an important topic- why does quantization come hand in hand with the uncertainty principle?





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