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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 $$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$ ...
22
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2answers
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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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2answers
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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, ...
17
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2answers
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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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5answers
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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 ...
19
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5answers
8k views

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 ...
11
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1answer
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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 ...
8
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2answers
2k views

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 ...
5
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3answers
661 views

How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states. Each one of them can be uniquely determined by total spin and its orientation, we can use $...
5
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3answers
3k views

What are the differences between indistinguishable and identical?

What is the difference between indistinguishable particles and identical particles?
12
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2answers
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Why is the phase picked up during identical particle exchange a topological invariant?

I've been wondering about the standard argument that the only possible identical particles in three dimensions are bosons or fermions. The argument goes like this: Consider exchanging the positions ...
18
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2answers
614 views

Geometric quantization of identical particles

Background: It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold $M^...
8
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4answers
597 views

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. ...
8
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3answers
759 views

How axiomatic is the symmetrization requirement (i.e. the Pauli principle)? (in QM)

I've so far always been told, that the symmetrization requirement is an axiom on the level of the Schrödinger equation and the statistical interpretation of the wave function (or it's absolute value). ...
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1answer
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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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11answers
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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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2answers
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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 ...
6
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2answers
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Bose Enhancement Factor

How may one explain the fact that the probability of a boson transferring to a state with an occupation number n is 'enhanced' by a factor of (1+n), compared to the classical case? (In the classical ...
21
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2answers
4k views

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 ...
3
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1answer
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Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by $$H=\frac{p_{1x}^2}{...
3
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1answer
138 views

Diagonal part of the configuration space of two indistinguishable quantum particles

Why is the configuration space of two indistinguishable particles given by $\frac{M^n-\Delta}{S_n}$? My question is about the $\Delta$. (Notation: $M$ is the configuration space of 1 particle. $M^n$ ...
2
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3answers
358 views

Why is Pauli exclusion principle necessary?

Why is it not possible to put two fermions in the same quantum state? I read in some book that this disturbs the quantum statistics. Also what makes bosons to have same quantum states?
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2answers
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multiverse fabric of reality

Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from ...
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2answers
865 views

Normalising multi-particle wavefunctions

For a quantum mechanical system of $n$ particles the state of the system is given by a wave function $\Psi (q_1, \dots , q_n)$. If the particles are indistinguishable, we demand that the swapping of ...
2
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1answer
193 views

Can two bosons be called identical although their momenta are different?

In my introductory book of Quantum Field Theory says that because of the conmutation of the creation operators for a two particles sistem, bosons can be called identical. They give an example using a ...
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1answer
130 views

Complete set of simultaneous eigenstates for identical particles

When I am learning about constructing wavefunctions for identical particles, I am taught to write down the wavefunctions of well defined energy then symmetrise them according to exchange symmetry. ...
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2answers
1k views

Total angular momentum in a full shell

I do not understand why it's supposed to be vanishing. Rather than discussing the question in its full generality I prefer to consider the following scenario, which I think sums up anything that's ...
0
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1answer
915 views

Eigenvalues of the exchange operator determined by the particle type (boson or fermion) in a two particle system

While dealing with a two particle system in QM (the particles are identical), the net wave function of the system would be simply the product of the wavefunctions of the individual particles in the ...
0
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1answer
313 views

Helium two particle system of identical particles

The equations [5.27]-[5.31] is a description of a two particle system (one electron, each in a hydrogenic atom). The assumption seems to be that these electrons are distinguishable (see equation [5.28]...