# Homework Help: Vacuum energy problem

1. Aug 5, 2007

### island

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.

2. Aug 5, 2007

### meopemuk

Could you please explain the physical problem you are trying to solve and the meaning of all symbols in your formulas?

Eugene.

3. Aug 5, 2007

### island

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!

4. Aug 5, 2007

### meopemuk

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?

Eugene.

5. Aug 5, 2007

### island

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
6. Aug 5, 2007

### meopemuk

OK. I have no idea what you are talking about. Good luck with your research!

Eugene.