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Text book question, need help.

  1. Apr 23, 2005 #1
    Hello all. Seems to be an excellent forum with many experts.

    I'm interested in quantum field theory. There's a question in my text book (introduction to QM and QFT) and I'm not sure if I found the right solution and its interpretation.

    Question 1: How many energy is needed to create a electron positron pair.
    Answer 1: (easy) 2*m(y)*c^2 where m(y) is the relativistic mass, you know.

    Question 2: Calculate the uncertainty relation between Energy and time.
    Answer 2: d(H)d(t)>=h/4pi (easy)

    And now there is the trickier part, a combination of these two. (the text book derived the discret energy values of the harmonic oscillator and shows that its ground state isn't zero).

    Question 11: The life time of a virtual e-e+-pair is given by the HUP and if there is a strong electric field in "empty" space with electromagnetic ground state oscillations how can the ground state oscillations create an e-e+-pair?

    my Answer: I tried to calculate this: [H,N] where H is the energy of the oscillation and N the number operator. I didn't find the solution of this and got [H,N]=0 (I think not the right one). My oppinion is: The N has to raise from 0 to 1 (to create a photon in vacuum). The "N" takes the needed energy for this from HUP. After this the photon interacts with the electric field and e-e+-pair will be created for time d(t) (HUP). After this happened the pair will annihilate and the N operator will lower (N=0) and the energy is given back to "empty" space.
    But as I got [H,N]=0 this can't be.

    Oh, please help me. There aren't answers in this book (only questions, well the most questions are easy, but that is a difficult one).
  2. jcsd
  3. Apr 23, 2005 #2
    Can nobody help?
  4. Apr 23, 2005 #3
    I don't know the answer to your problem, but try typing:

    "uncertainty relation" "energy and time"

    into Google. Stuff does come up that may help you.
  5. Apr 23, 2005 #4
    Sorry, but I coudn't find what I looked for.
  6. Apr 24, 2005 #5
    Does nobody know this?
  7. Apr 25, 2005 #6
    Question 2: Ground state has energy what ever you want. Only energy shifts are measurable quantities.

    Question 11: I dont understand what you are trying to say. It looks like non-Relativistic QM + creation of virtual particles (!?). Bad combination. The only thing I can understand is [H,N]=0. Which is true in, otherwise how would you get the energies of the harmonic oscilator?
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