Solve Momentum Expectation Change w/ Ehrenfest's Thm

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SUMMARY

The discussion centers on applying Ehrenfest's theorem to determine the time rate of change of the expectation value of momentum when given a Hamiltonian of the form iA(p + c). The key point is that the momentum operator p should be treated as an operator within the commutator [p, H], rather than as a numerical value. This distinction is crucial since the commutator of an operator with itself results in the zero operator, which simplifies the analysis of the system's dynamics.

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  • Understanding of quantum mechanics principles, particularly operators and Hamiltonians.
  • Familiarity with Ehrenfest's theorem and its applications.
  • Knowledge of commutation relations in quantum mechanics.
  • Basic proficiency in linear algebra, specifically with matrices and operators.
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If I had a hamiltonian of the form iA(p + c), where A is a constant matrix, p the momentum operator and c an ordinary constant how do I find the time rate of change of the expectation momentum value?
I've tried using Ehrenfest's theorem but I don't understand whether in [p,H], I should treat p as an operator or as an ordinary number? Could someone please make this clearer to me? Thanks.
 
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P is an operator in the commutator. Its commutator with itself is the zero operator.
 

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