Generating functional for harmonic oscillator

Generating functional for harmonic oscillator

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4 Responses to Generating functional for harmonic oscillator

  1. Pedro Dardengo Mesquita says:

    Sorry, I will reformulate it.
    To get a deeper understanding I suggest reading:

    R. W. Fuller, S. M. Harris, and E. Leo Slaggie, S-Matrix Solution for the Forced Harmonic Oscillator, American Journal of Physics 31, 431 (1963)
    https://aapt.scitation.org/doi/pdf/10.1119/1.1969575

    In this article a full solution of the problem is given, the matrix elements:

    The expected value of an excited state with the ground state is calculated, setting the excited to zero is the solution of the problem in the book.

    The solution to the expected value of two excited states is not given in full detail since its more difficult to work out Wick`s theorem in this case.

    Also physical interpretations are given.

    No mention is made to Feynman diagrams, but it is shown why only even terms survive.

    Thank you.

    Like

  2. Pedro Dardengo Mesquita says:

    To get a deeper understanding I suggest reading:

    R. W. Fuller, S. M. Harris, and E. Leo Slaggie, S-Matrix Solution for the Forced Harmonic Oscillator, American Journal of Physics 31, 431 (1963)
    https://aapt.scitation.org/doi/pdf/10.1119/1.1969575

    In this article a full solution of the problem is given, the matrix elements:

    is calculated, j=0 is the solution of the problem in the book.
    OBS.: I still can get my head to work with collecting all terms that survive Wick`s theorem in this case, but maybe its no problem to you.

    solution is stated since its more difficult to work out Wick`s theorem in this case.

    and physical interpretations are given.

    No mention is made to Feynman diagrams, but it is shown why only even terms survive.

    Thank you.

    Like

    • Pedro Dardengo Mesquita says:

      somehow some words didn`t appear, so I said that the solution of the matrix elements of S(j,0) is given, and the solution of S(j,k) is stated

      Like

      • growescience says:

        Sorry, but it looks like some bits of your original comment are still missing. Could you copy and paste the original and fill in the missing bits, please?

        Like

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