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Homework Help: Vacuum energy problem

  1. Aug 5, 2007 #1
    e−iHT=1→H=2πn/T=ωn ; n=0, ±1, ±2, . . . .

    I'd like to set the vacuum energy at 1/2ω, while requiring e-iHT=−1, and that the negative energy states be filled, as well, although, this may require further explanation.

    Can somebody please help me?
  2. jcsd
  3. Aug 5, 2007 #2
    Could you please explain the physical problem you are trying to solve and the meaning of all symbols in your formulas?

  4. Aug 5, 2007 #3
    This is the spectrum of a quantum harmonic oscillator, except for the emergence of negative energy states, with n<0. A "Vacuum energy" of 1/2ω arises if we require that e-iHT=−1 and just realized that I've answered my own question, thanks!
  5. Aug 5, 2007 #4

    You are welcome.
    Though I am curious, what is the physical meaning of the negative energy states, and how did you get this equation e-iHT=−1?

  6. Aug 5, 2007 #5
    Okay, my knowledge of this is too specific if not limited, but...

    The "extra" 1/2 in the eigenvalues of the harmonic oscillator Hamiltonian can be thought of as having a phase factor of -1, which *can* represent vacuum energy as rarefied mass-energy that has a negative pressure, (-0.5*rho(matter)*c^2), in the cosmological model that I am thinking about.
    Last edited: Aug 5, 2007
  7. Aug 5, 2007 #6
    OK. I have no idea what you are talking about. Good luck with your research!

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