Commuting vs Noncommuting Operators in Quantum Mechanics, and the Commutator between Them

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Quantum Chemistry Problem [Q20-04-00]. Fundamentals of Quantum Mechanics. What are Commuting versus Noncommuting Operators? Why does Operator Commutation matter in Quantum Mechanics? Definition of the Commutator and how to calculate the commutator explicitly.
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Question:
Find the commutator for the operators, x² and d²/dx².
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