Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Text book question, need help.
  1. Text book mistake? (Replies: 5)

Loading...