# Questions tagged [identical-particles]

Questions related to the discernibility of many-body systems, its philosophical implications and its mathematical description.

168 questions
Filter by
Sorted by
Tagged with
0answers
13 views

### Validity of the Born approximation for identical-particle scattering

My understanding of the Born approximation is that it valid for scattering with small momentum transfer. In the context of two-particle, isotropic, elastic scattering, I would trust the Born ...
0answers
16 views

### Are atoms in a perfect crystal lattice indistinguishable?

So I was reading a wikipedia article about the third law of thermodynamics, and was intrigued by the following sentences: Suppose a system consisting of a crystal lattice with volume V of N ...
4answers
888 views

### Distinguishable, indistinguishable paramagnetic ideal gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
2answers
201 views

### How to write equation of state in terms of partition function?

While studying quantum gases (fermions, bosons), equation of state written were $PV = k_B T Z_{gr}$, where $Z_{gr}$ is the partition function of grand canonical ensemble. $P$ and $V$ are pressure and ...
3answers
68 views

### Appropriate space in second quantization

The appropriate space for the study of a system of identical bosons, for instance, is something like \begin{equation} \tag{1} \mathbb{C}\oplus\mathcal{H}\oplus(\mathcal{H}\otimes\mathcal{H})_S\oplus(...
2answers
23 views

### Orbital wavefunction for a system of two electrons

I am new to this forum! I write here hoping someone can help me. I have found a statement in my quantum mechanics book that I really don't understand. We have a system of two electrons. If both are ...
0answers
49 views

### Are parahydrogen and orthohydrogen identical particles?

I have no formal physics background, just aerospace engineering, and I'm working on a DSMC project simulating relaxation of hydrogen in non-equilibrium, rarefied, 1D flow via translational and ...
0answers
59 views

2answers
72 views

### Confusion regarding indistinguishability of particles and the definition of Gibbs entropy

I have been reading about the Gibbs paradox, in which the assumption that particles of a monoatomic ideal gas are distinguishable leads to a paradox in which entropy is not extensive. In Schroeder's ...
1answer
599 views

### When is separating the total wavefunction into a space part and a spin part possible?

The total wavefunction of an electron $\psi(\vec{r},s)$ can always be written as $$\psi(\vec{r},s)=\phi(\vec{r})\zeta_{s,m_s}$$ where $\phi(\vec{r})$ is the space part and $\zeta_{s,m_s}$ is the spin ...
1answer
113 views

2answers
491 views

### Typical application of Pauli exclusion principle in atoms

Typically when we talk about the electron orbitals around atoms we talk about them getting "filled up" starting with s1, s2, and so on (with spin taken into account as well). This relies on the Pauli ...
4answers
310 views

### The wave function of a system of two identical particles

For a system of two identical particles, where $r_1$ is the position vector of particle 1 and $r_2$ is the position vec. of particle 2, the wave function should be one of the plus or minus states: \...
4answers
409 views

### Why triplet and not singlet?

Quoting from Eisberg Resnick Quantum Physics: If we consider space variables of two electrons (identical particles) to have almost the same values, then their wavefunctions are 'almost' identical ...
1answer
52 views

### When exactly do identical fermions interact?

For the case of $N$ identical fermions in a three-dimensional box, the Pauli Exclusion Principle necessitates that the overall wavefunction of the system is antisymmetric. No two fermions can occupy ...
5answers
6k views

### Are black holes indistinguishable?

In the standard model of particles it is understood that besides characteristics like momentum, spin, etc., two electrons are indistinguishable. Are two black holes, in the same sense, ...
0answers
202 views

### Do the exchange operator and Hamiltonian commute for non-identical particles?

Wherever I have read about exchange operator(P), it is stated that for two identical bosons it introduces a plus sign after exchange and minus sign for fermions. P and Hamiltonian(H) commute for two ...