All Questions
6
questions
2
votes
1
answer
310
views
Statistical Mechanics: Particles on a Sphere
$K$ identical particles of mass $m_0$ are bound to move on a sphere of radius R. The system is at equilibrium at temperature $T_0$.
1 - What's the internal energy ($E$)?
2 - What's the specific heat ...
- 23
0
votes
0
answers
186
views
Find partition function for a classical harmonic oscillator with time harmonic forcing
I have been trying to find partition function for classical harmonic oscillator with time harmonic forcing term and reached an expression. I want to know if I am correct.
There is abundant ...
- 595
1
vote
1
answer
458
views
canonical ensemble that is quantum mechanical and continuous?
I do not understand what the following statements from Wikipedia mean
For a canonical ensemble that is quantum mechanical and continuous, the canonical partition function is defined as
$$ Z = \...
- 2,107
2
votes
2
answers
575
views
Partition function of a 3D vibrating string
Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both?
$$
Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k}
$$
or
$$
Z_{\text{...
- 2,107
1
vote
0
answers
2k
views
Partition function microcanonical ensemble
I was wondering if there is a way to understand the partition function for a microcanonical ensemble $$\mathcal Z(E)=\sum_{\text{microstate $i$ with energy $E$}} w_i$$
as a limit of the continuous ...
- 97
1
vote
1
answer
2k
views
Calculation of the partition function for a classical 2D gas lying on the surface of a sphere of constant radius $R$
I'm kind of confused with this system. My first question is. Is the Hamiltonian of one particle of this gas the following?
$$H(x,y,z,p_{x},p_{y},p_z)=\frac{1}{2m}\left(p_{x}^{2}+p_{y}^{2}+p_{z}^{2}\...
- 1,373