Solving Vacuum Energy Problem: e-iHT=-1, 1/2ω, Fill Negative States

[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.

Can somebody please help me?

 

[meopemuk]

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?

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

Eugene.

 

[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!

 

[meopemuk]

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!

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.

 

[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.

 

[meopemuk]

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.

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

Eugene.