# Questions tagged [identical-particles]

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

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### Why is the partition function divided by $(h^{3N} N!)$?

When computing partition functions for classical systems with $N$ particles with a given Hamiltonian $H$ I've seen some places writing it as $$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$ ...
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### Are all electrons identical?

Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very ...
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### What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
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### Gibbs Paradox - why should the change in entropy be zero?

The Gibbs paradox deals with the fact that for an ideal gas with $N$ molecules in a volume $V$ seperated by a diaphragm into two subvolumes $V_1,V_2$ with $N_1,N_2$ particles in each subvolume, ...
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### How are anyons possible? (another version)

I know that this question has been submitted several times (especially see How are anyons possible?), even as a byproduct of other questions, since I did not find any completely satisfactory answers, ...
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### Why doesn't the entropy increase when two similar gases mix with each other?

Entropy increases when two substances mix with each other. For example, the entropy of mixing of two different gases are given by $$\Delta S= 2Nk\ln\frac{V_f}{V_i}\;.$$ But, the entropy doesn't ...
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### Why must fermions be antisymmetric? [closed]

I have read that fermions cannot exist in the same state simultaneously. I understand why indistinguishable particles with an antisymmetric superposition of states can't exist in the same state ...
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### Making indistinguishable particles distinguishable?

I am wondering if we fix the locations of indistinguishable particles, will the identical particles become distinguishable? Say, put each one of the indistinguishable particles into a small box. ...
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### When are two fermions considered identical?

I am a bit confused about the terminology concerning identical fermions. In quantum mechanics, identical fermions need to obey certain anticommutation relations i.e. have an antisymmetric total ...
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### What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
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### Same photon or different photon?

Consider a typical optical focusing system: A small light source, then a collimating lens, then a focussing lens, and then a detector (e.g. CCD). Assume that source intensity is so low that only one ...
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### Why two spin-$1$ bosons could not be in a spin $\frac{1}{\sqrt{2}}(|1,0\rangle-|0,1\rangle)$ state?

Consider two boson of spin $1$ without angular momentum. I'm seeing an argument that "because those two particles were bosons, they must be symmetric under the exchange $m_1,m_2$. Thus they could ...
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### About the factorial N! in the partition function

After reading these posts: Why is the partition function divided by $(h^{3N} N!)$?, What is the resolution to Gibb's paradox?, and these articles: The Gibbs Paradox and the Distinguishability of ...
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### Theoretically, could there be different types of protons and electrons?

Me and my friend were arguing. I think there could theoretically be different types of protons, but he says not. He says that if you have a different type of proton, it isn't a proton, it's something ...
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### Is there is a reason for Pauli's Exclusion Principle?

As a starting quantum physicist I am very interested in reasons why does Pauli's Exclusion Principle works. I mean standard explanations are not quite satisfying. Of course we can say that is because ...
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### Indistinguishable particles when wavefunctions don't overlap

My question is the following : Imagine that we study two electrons, one has spin up and the other down. If the two wavefunctions overlap, then I have the symetrisation postulate that occurs, the ...
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### Are protons and neutrons affected by the Pauli Exclusion Principle?

I'm very confused about the Pauli exclusion principle. Wikipedia states it as "two identical fermions cannot occupy the same quantum state in a quantum system". I understand this for electrons that ...