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

Click For Summary

Homework Help Overview

The discussion revolves around the concept of vacuum energy in the context of quantum mechanics, specifically relating to the quantum harmonic oscillator and the implications of negative energy states. The original poster seeks assistance in understanding the conditions under which the vacuum energy can be set at 1/2ω while also considering the filling of negative energy states.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the vacuum energy and the spectrum of the quantum harmonic oscillator, questioning the physical meaning of negative energy states and the derivation of the equation e-iHT=−1. Some participants express uncertainty about the implications of these concepts.

Discussion Status

The discussion is ongoing, with some participants offering insights into the nature of vacuum energy and its representation in cosmological models. However, there remains a lack of consensus on the interpretation of negative energy states and their significance.

Contextual Notes

Participants note the need for clarification on the physical meanings of symbols and equations used in the discussion, indicating that some foundational understanding may be required to fully engage with the topic.

island
Messages
42
Reaction score
0
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?
 
Physics news on Phys.org
island said:
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.
 
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!
 
island said:
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.
 
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:
island said:
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.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 2 ·
Replies
2
Views
10K
  • · Replies 2 ·
Replies
2
Views
3K