Zwiebach Page 194 Q11.3: Understanding "Viewing" a Time-Dependent Heisenberg Op.

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SUMMARY

The discussion centers on Quick Calculation 11.3 from Zwiebach's text, specifically regarding the interpretation of "viewing" the operator x_0^I as an explicitly time-dependent Heisenberg operator as defined in equation (11.38). Participants express confusion over the term "viewing" and its implications for understanding the time dependence of x_0^I. A proposed solution involves rewriting equation (11.38) to demonstrate that the derivative with respect to time τ is zero, indicating a lack of explicit time dependence.

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  • Understanding of Heisenberg operators in quantum mechanics
  • Familiarity with Zwiebach's textbook, particularly equations (11.38) and related concepts
  • Knowledge of time dependence in quantum mechanics
  • Basic calculus, specifically differentiation with respect to time
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Students of quantum mechanics, particularly those studying Heisenberg operators and their time dependence, as well as educators seeking to clarify concepts from Zwiebach's textbook.

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Homework Statement


I am confused about Quick Calculation 11.3. What does he mean "by viewing x_0^I as the explicitly time-dependent Heisenberg operator defined by (11.38)"?

Specifically, what does "viewing" mean?


Homework Equations





The Attempt at a Solution

 
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This one is not clear to me either. However, what I did was assume that [itex]x_0^I[/itex] does have explicit time dependence by rewriting equation (11.38) on page 193 as

[tex]x_0^I(\tau) = x^I(\tau) - \frac{p^I}{m^2}\tau[/tex]

and then showing that the derivative w.r.t. [itex]\tau[/itex] is zero. It's not hard enough to justify a QC though.
 

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