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If G is an operator corresponding to a physical quantity and H is its Hamiltonian, then the commutator relation \([G, H] = 0\) tells us that

Question and options

If G is an operator corresponding to a physical quantity and H is its Hamiltonian, then the commutator relation [G,H]=0[G, H] = 0 tells us that
  1. G is not a physical entity
  2. G is a constant of motion
  3. G varies with time
  4. H is not a constant of motion

Answer and explanation

Correct answer: B - G is a constant of motion
By Heisenberg's equation dGdt=iℏ[H,G]\frac{dG}{dt} = \frac{i}{\hbar}[H,G] + explicit time derivative; if [G,H]=0[G,H]=0 (no explicit time dependence) GG is conserved, i.e. a constant of motion.

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