Commute Operators: Hi Niles - Find Out Now

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The discussion centers on the commutation relations between creation/annihilation operators for fermions, denoted as c and its adjoint, and the exponential operator exp(-iHt), where H represents the Hamiltonian of the system. Niles confirms that these operators do not commute, providing the relationship H = k c*c and the anticommutation relation {c, c*} = 1, leading to the conclusion that [H, c] = -k c. This establishes a clear understanding of the non-commutative nature of these operators in quantum mechanics.

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  • Knowledge of Hamiltonians in quantum systems
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Niles
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Hi

Say I have the creation/annihilation operators for fermions given by c and the exponential operator exp(-iHt), where H denotes the Hamiltonian of the (unperturbed) system. Is there any way for me to find out if exp(-iHt) and c (and its adjoint) commute?Niles.
 
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Niles said:
Hi

Say I have the creation/annihilation operators for fermions given by c and the exponential operator exp(-iHt), where H denotes the Hamiltonian of the (unperturbed) system. Is there any way for me to find out if exp(-iHt) and c (and its adjoint) commute?


Niles.
They don't commute, H = k c*c and {c,c*} = 1, therefore [H, c] = - k c. You can work out the rest.
 

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