Significance of the hamiltonian commuting

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SUMMARY

The significance of an operator commuting with the Hamiltonian lies in the conservation of the corresponding physical quantity over time. If a state is an eigenstate of this operator at time t=0, it will remain an eigenstate at any later time due to the Hamiltonian's role in governing the system's time evolution. This principle is crucial in quantum mechanics, as it establishes the relationship between observables and their conservation laws.

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sridhar
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Wht is the significance of an operator commuting with the hamiltonian??
Its definitely more than them being measurable simultaneously and precisely!
 
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sridhar said:
Wht is the significance of an operator commuting with the hamiltonian??
Its definitely more than them being measurable simultaneously and precisely!

It means that this physical quantity is conserved in time. In other words, if a state is an eigenstate fo this other operator at t=0, it will remain an eigenstate of that operator at later time. This is because the Hamiltonian is the operator that governs the time evolution of the system.
 

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