Questions tagged [virial-theorem]
In mechanics, the virial theorem relates the average over time of the total kinetic energy, <T>, of a stable system consisting of several particles bound by potential forces, with that of the total potential energy, <V>.
101
questions
0
votes
1
answer
46
views
Is the Virial Theorem dependent on the classical Equipartition Theorem?
The Wikipedia entry for the Virial Theorem states:
"*The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems ....
- 6,102
1
vote
3
answers
103
views
Use of time average in the Virial Theorem
I was trying to understand how to derive the Virial Theorem. I found a YouTube video explanation (https://www.youtube.com/watch?v=zwsmyYnyuj8) where the person took a time average of the second ...
- 45
2
votes
1
answer
62
views
The Virial Theorem and Long-Range Repulsion
I am working on a problem (the 12th problem in the third chapter of the third edition of Goldstein's Classical Mechanics) that asks the reader to consider certain long-range interactions between atoms ...
- 373
1
vote
1
answer
71
views
Virial theorem for many-body systems under closed systems
I am reading Wolfgang Nolting's Theoretical
Physics 1, the book reads:
$$
2\langle T\rangle=\left\langle\sum_i \vec r _i \cdot \nabla_i V\right\rangle
$$
The right-hand side is the so-called virial ...
- 77
4
votes
1
answer
293
views
Virial Theorem for Gas Particles
My statistical mechanics professor stated the Virial Theorem as
\begin{equation}
\langle K \rangle = -\frac12 \sum_{i=1}^N \langle \mathbf{F}_i\cdot \mathbf{r}_i\rangle
\end{equation}
For an ideal gas ...
- 333
1
vote
1
answer
60
views
Virial theorem for momentum fluctuations
In the paper https://journals.aps.org/pr/abstract/10.1103/PhysRev.109.1464 Lebowitz attempted to derive an estimation of the magnitude of center of mass momentum fluctuations in the presence of ...
- 895
2
votes
2
answers
200
views
Derivation of Kepler's third law using Virial theorem
I am familiar with the long derivation of Kepler's third law using the equations of motion. One starts with
\begin{equation}
\dot{r}=\sqrt{\frac{2}{m}\big[E-V(r)\big]}
\end{equation}
and integrates to ...
- 4,827
1
vote
1
answer
97
views
Dark energy contributing to, or modifying, mass estimates?
I have found some papers (like this one: https://www.aanda.org/articles/aa/full_html/2009/45/aa12762-09/aa12762-09.html) which say that dark energy increases the potential energy in a system of a ...
- 2,462
1
vote
2
answers
484
views
Conditions for the Virial theorem
I've been investigating the Virial Theorem, and I've found different conditions, some more restrictive than others, for it to be applicable to a given system. According to my professor, said theorem ...
- 1,616
3
votes
0
answers
146
views
Is there a Virial theorem in General Relativity?
I know that in Newtonian mechanics one can derive the virial theorem for $N$ gravitating particles
\begin{equation}
2\langle T\rangle=-\langle U\rangle
\end{equation}
where $T$ is the kinetic energy ...
- 4,827
0
votes
1
answer
39
views
Where can you find the velocity dispersions of globular clusters?
I'm trying to use the Virial theorem to determine the mass of the M5 cluster and I need the velocity dispersion to calculate this. Does anyone know where I can find a table with these velocity ...
4
votes
1
answer
264
views
Does the Hartree Fock energy of a virtual orbital fulfill the virial theorem?
In calculating the ground state of atoms or molecules at the equilibrium geometry, the expectation values of the kinetic, $⟨T⟩$, and potential, $⟨V⟩$, energies relate to the total energy, $E$, ...
- 129
0
votes
1
answer
186
views
How did Zwicky discover dark matter?
According to Wikipedia Zwicky used "virial theorem" to discover the gravitational anomaly in the Coma Galaxy cluster. But I also remember reading that he used Kepler's third law. Which one ...
- 217
7
votes
2
answers
186
views
The eigenfunctions of $H =\frac{p^2}{2m}+ V_0 \log(|x|/a)$ and a curious virial theorem result
I'm thinking about applications of the virial theorem to $1d$ quantum systems. The statement of the virial theorem is that all bound states of the Hamiltonian $T+V$ satisfy the constraint
$$\langle 2 ...
- 2,292
8
votes
6
answers
2k
views
How is thermal energy split between kinetic energy and potential energy?
Internal ("thermal") energy must be some combination of kinetic energy and potential energy, although most discussions of internal energy mention only the kinetic energy. However you also ...
- 141