Problem 19.1 Peskin: Find Harmonic Oscillator Solution

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Discussion Overview

The discussion revolves around Problem 19.1 from Peskin's QFT book, specifically focusing on the derivation of a harmonic oscillator solution from a given ansatz. Participants are examining the mathematical steps involved and the implications of the resulting equations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about not obtaining a harmonic oscillator equation when substituting the ansatz into the equation provided in the problem.
  • Another participant asserts that the problem is clear and provides the equation and ansatz involved, indicating that the expected outcome should be a harmonic oscillator equation.
  • A different participant points out that not everyone has access to Peskin's book, suggesting that some may not be able to refer to the problem directly.
  • Another participant claims that a harmonic oscillator is obtained at every ##x^1##, with the frequency depending on that coordinate, implying a potential misunderstanding of the problem's requirements.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus. There are differing views on the clarity of the problem and the nature of the solution, with some asserting the existence of a harmonic oscillator solution while others express confusion about the derivation.

Contextual Notes

Some participants note the dependence of the frequency on the coordinate ##x^1##, which may complicate the interpretation of the harmonic oscillator solution. There is also an implication that assumptions about access to the text may affect the discussion.

JCCJ
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Hi,
I'm trying to do this problem (19.1 from Peskin) that apparently should be quite straightforward but when I plug the anzat given at c) into the equation I don't get an harmonic oscillator as the book indicates. Could please anyone tell me what is wrong?
Thanks
 
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This is a first - not only does the student not type the answer, he doesn't even type the question!
 
I think the question/problem is quite clear: The problem 19.1 from the peskin QFT book. I give as a fact that anyone in the high energy physics section has acces to this book to refer to the problem.
Anyway the problem is the following:
given the equation -i \sigma \cdot D \psi_R=0, where A^{\mu}=(0,0,B x^1, A) with B a constant and A depends only adiabatically in time.
Now when I put the anzat given by the book \psi_R=\left(\begin{array}{c}\phi_1(x^1)\\ \phi_2(x^1)\end{array}\right)e^{i(k_2x^2+k_3 x^3)} and eliminate one of the \phi I'm supossed to get an harmonic oscillator eqn. How? I get an eqn of the form \phi_i ''(x^1)+\omega^2(x^1) \phi_i(x^1)=0 with an explicit dependence of \omega in x.
 
Not everyone is within arm's reach of Peskin. I don't even own a copy.
 
You get a harmonic oscillator at every ##x^1##, where the frequency depends on that coordinate.

By the way: with -tags, you don't get new lines for every symbol.
 

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