All Questions
Tagged with momentum statistical-mechanics
14
questions
0
votes
1
answer
77
views
Definition of temperature as variance of the momentum
I have always taken the definition of temperature to be the kinetic energy Statistical mechanics definition of temperature as the average kinetic energy.
However I have been reading a paper where the ...
- 101
1
vote
1
answer
141
views
How to justify (mathematically and physically) the total momentum in many-body physics?
If we have a many-body sistem and we study the limit with infinite particles (we may decide for example to have a fixed constant density), I am trying to understand how classical mechanics and quantum ...
- 159
2
votes
0
answers
94
views
How is linear momentum conserved in a cooling gas?
Consider a closed cylindrical tank with no external forces acting on it which is filled with gas which is cooling due to radiative heat loss to the surroundings. Consider a smaller tank at a higher ...
- 31
0
votes
1
answer
71
views
Infinitesimal momentum element
I understand that $d^3x$ is an infinitesimal volume element. But how do I physically make sense of $d^3p$, the momentum element?
- 1,222
0
votes
0
answers
37
views
Is there any quantum operator for mode as there is for mean?
I am quite familiar with the position and momentum operators and expectation value or simply the average position or momentum
But sometimes experiments may require the mode too. But that is only ...
- 1,333
0
votes
0
answers
33
views
Physical meaning of this integral in $k-$space [duplicate]
I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of ...
- 131
0
votes
0
answers
188
views
Physical meaning of this integral in $k$-space
I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of ...
- 131
3
votes
1
answer
198
views
Why is the constraint when maximizing entropy on energy rather than momentum?
State in classical mechanics is specified by the position and the momentum. Yet, in statistical mechanics, the usual approach is to maximize the entropy of a system subject to an energy constraint. ...
- 133
1
vote
1
answer
318
views
Why do we use momenta and not velocities in the partition function of statistical mechanics?
The question is in the title, what follows is an example.
Consider for example a free classical particle in a 1D box of length $L$ in contact with a thermal reservoir. According to Boltzmann the ...
- 28.3k
3
votes
0
answers
124
views
Conservation of momentum in statistical physics in presence of a potential
Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ...
- 337
2
votes
2
answers
596
views
Microcanonical Ensemble - probability of finding momentum
I was trying to calculate the probability of finding a particle with momentum $p$ in the microcanonical ensemble in a 3-dimensional box.
$$\rho_i(\vec p)= \langle\delta(\vec p - \vec p_i)\rangle= \int ...
0
votes
1
answer
309
views
Momentum distribution function for a particle in a 1D box
In these notes on statistical thermodynamics (pp. 62), I encountered this [topic: particle in a 1D box]:
We shall adopt the initial condition that the probability distribution function
has the ...
- 147
0
votes
1
answer
2k
views
Sum over momentum states
In our lecture we used quite a couple of times that the sum over momentum states can be approximated by an integral over them.
But instead of substituting $\sum_p \rightarrow \int d^3p$, we replaced ...
- 1,880
0
votes
1
answer
376
views
What's wrong with this simple derivation of energy flux in a photon gas?
In a photon gas, we know that pressure, $P$, and energy density, $u$, are related by:
$$P=\frac{u}{3}$$
We also know from relativity that the momentum of a photon is
$$p=\frac{E}{c}$$
Finally, the ...
- 1,688