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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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Physical meaning of symmetric and antisymmetric wavefunction

On describing Bosons and Fermions, the symmetry of wavefunction is introduced first. Here, If two particles a and b, are in two states n and k respectively, we get the wavefunction individually. On ...
Rajesh R's user avatar
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2 answers
101 views

What exactly does it mean for two bosons to be in the same state?

If I understand QM correctly, it's a fact that two bosons can have the same wave function in principle. What I'm wondering is if the particles governed by the wave functions can also be in the same ...
Francisco Skrobola's user avatar
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1 answer
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Symmetrizing of projectors with identical particles

I am dealing with systems of $N$ identical particles in quantum mechanics. The tensor product state space is : $V^{\otimes N}$. (in the question is use the term symmetrized to designate either ...
cmatteo's user avatar
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Is it possible that a macroscopic object tends to a separable state without the need for objective collapse?

For a multi-particle system, superposition is in some sense equivalent to entanglement; with the Dirac field being treated as classical under second quantization, for example, we could at least argue ...
Adam Herbst's user avatar
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Is indistinguishability required for the stability of matter?

Classically, it is well-known that a charge-neutral system of electrons and nuclei is thermodynamically unstable. In simplistic terms, nothing in classical mechanics prevents electrons from binding ...
Endulum's user avatar
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Net dipole moment of identical-particle system [closed]

Let $N$ identical electric charges be arranged arbitrarily in space, in such a way that each of them has a fixed position $\vec{r}_i$, a charge $q$ and a mass $m$. If I were to calculate the total ...
Lagrangiano's user avatar
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1 answer
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Distinguishability in Maxwell-Boltzmann statistics

Per the Wikipedia page on Maxwell-Boltzmann statistics, the mean occupation number describes the average number of particles in the i-th single-particle state for distinguishable particles. To be ...
TheorVHP's user avatar
2 votes
1 answer
41 views

Fermi-Dirac Distribution for Multiple Species

If I have a system containing two types of fermions, what is the probability of a state of energy $E$ being occupied? Is it just the sum of two standard Fermi probabilities for each type of fermion?
S.T. Zweig's user avatar
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1 answer
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Is a fermionic boson possible?

We know that bosons need an overall symmetric wavefunction. So is it possible for a boson to have an anti-symmetric spatial wavefunction and an anti-symmetric spin wavefunction? Such that upon ...
Despaxir's user avatar
2 votes
0 answers
40 views

Is the overall (distinguishble-particle) ground state for a many-body identical particle Hamiltonian also immediately the bosonic ground state?

Consider the following many-body Hamiltonian of $N$ particles in an external trapping potential with inter-particle interactions: \begin{align} \hat{H}= \sum_{i=1}^{N} \left[-\frac{\hbar^2}{2m} \...
Coffee-7's user avatar
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2 answers
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Calculation of canonical partition function for fermion system with degenerate energy levels

I'm having trouble in visualising the generalized version of the question asked here. We have a system with levels whose energies are $0, \epsilon, 2 \epsilon, ..., n\epsilon$, and the number of ...
Alan Whitteaker's user avatar
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If the state is VH+HV how one can prove experimentally that two photons are identical?

From a SPDC source we get two photons in a $|VH\rangle+|HV\rangle$ state. How is to be proven experimentally that they are identical while one would be in $|H\rangle$ and the other in $|V\rangle$ ...
Mercury's user avatar
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Since anyons cannot exist in our 3+1D world, what does it mean to have discovered them? Why should we study them?

There have been previous questions on this, for example see this and this question, but my question is different. I get that in 2+1D, mathematically speaking, exchanging two identical particles twice ...
Prem's user avatar
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Normalization of one particle state wave function in fock space - commutator

In deriving the 1/$\sqrt{N!}$ normalization factor the first step is looking at the one particle state (see image below). I am confused about how we got from the first line to the second? Maybe I am ...
choochoochooo's user avatar
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0 answers
64 views

Operator that gives a permutational symmetry factor

Suppose that we have a system with $N$ bosonic modes, meaning that there is a vacuum state $|0\rangle$ and a set of $N$ pairs of creation-annihilation operators $a_i$ and $a^{\dagger}_i$. When ...
V. Asnin's user avatar
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0 answers
30 views

Grand canonical partition function for Bose-Einstein statistic and Maxwell-Boltzmann statistics for indistinguishable particles

If we have N non-interacting particles and N assumes the values 1 and 2.They can be found in three energy levels $\epsilon_{l}=\epsilon*l$ with l = 0, 1, 2. I tried to write the function as Z(µ, T)=$\...
Mario's user avatar
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1 answer
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Double slit: how identical is identical?

It works even with C60 molecules... The authors of the above article already wrote in the abstract: "Of particular interest is the fact that C60 is almost a classical body, because of its many ...
Hauke Reddmann's user avatar
2 votes
1 answer
75 views

Interacting identical bosons

Say we have two spin-1 bosons on a ring of circumference L, where they interacts according to the potential $g\delta(x_1-x_2)$ (g is a real number). What is the degeneracy of the first excited state? ...
Tachon's user avatar
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Can spin orientation change with the excitement?

Let's say we have a 1 dimensional square well system with 2 electrons. In the ground state , the only possible spin state is the singlet. So that means one of the electrons should be up and the other ,...
Özge's user avatar
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5 votes
2 answers
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How can two electrons form the anti-symmetrical state?

Suppose that I have two electrons in a box that were originally spread by a infinite potential wall. The two electrons are in their ground state wave function (sine function). Now I removed the ...
Neon slayer 's user avatar
1 vote
1 answer
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Does a lump of baryonic matter have a well-defined particle number?

From reading about quantized electromagnetism, it seems that many forms of light (e.g. lasers) don't have well-defined numbers of photons, or in other words are superpositions of different number ...
Jamie S's user avatar
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Understanding Dirac's argument for the indistinguishability of electrons

In his paper 'On the theory of quantum mechanics' (1926), Dirac makes the following argument for why electrons should be considered indistinguishable: Consider now a system that contains two or more ...
APK92's user avatar
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2 votes
1 answer
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Twisting internal/external lines in Feynman diagrams. How does it result in different diagrams?

I'm following Griffiths' Introduction to Elementary Particles. To introduce the Feynman rules, he proposes ABC theory, where these three spin-$0$ particles interact through a fundamental vertex: One ...
blundered_bishop's user avatar
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1 answer
135 views

Scalar Product Calculation and Identical Particles in Quantum Mechanics

In the book "Nolting, Theoretical Physics Part 5/2" (German), on Page 264, Formula 8.80, the author introduces second quantization in the case of identical particles. One considers the ...
Mad's user avatar
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1 answer
387 views

Do exchange operators commute?

I am new to quantum mechanics so please excuse the question if its answer is obvious. Given an ensemble of $N$ identical particles and the exchange operators $U_{\alpha, \beta}$ and $U_{\alpha, \gamma}...
velo's user avatar
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1 vote
1 answer
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Does Quantum Heisenberg Spin Model obey Fermi-Dirac or Bose-Einstein statistics? [closed]

Does Quantum Heisenberg Spin Model obey Fermi-Dirac or Bose-Einstein statistics? We want to study a $N$-Spin Quantum Heisenberg Spin chain: Hamiltonian is: $$\displaystyle {\hat H}=-J\sum _{{j=1}}^{{...
david's user avatar
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6 answers
318 views

Definition and Resolution of the Gibbs paradox in thermodynamics

The entropy of an ideal gas is known to be $$S(V,T)=S_{0}+nR\log \left|\frac{V}{V_0}\right| +C_v\log\left| \frac{T}{T_0}\right|.$$ Now let us have a cylinder of volume $V=V_1+V_2$ separated by an ...
TomS's user avatar
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1 vote
1 answer
397 views

Identical particles system with center of mass and relative coordinates

In order to properly express my doubts, I am afraid that I will need an introduction a bit longer than usual, so my apologies in advance for that. It is a doubt in non-relativistic quantum mechanics, ...
MBlrd's user avatar
  • 159
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1 answer
89 views

Is QFT linear with respect to superposition of multi-particle states?

I saw other posts such as this one but I don't think it's quite the same question, or even if it is, the answer employs the operator formalism and I'm not sure I follow it. I'm wondering, if you have ...
Adam Herbst's user avatar
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0 answers
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How can Anyons be Possible? [duplicate]

I'm studying Identical Particles in Quantum Mechanics and somewhere I saw that some particles, called Anyons, can generalize the concept of Fermions and Bosons, showing a symmetry under permutation ...
Ruffolo's user avatar
  • 378
3 votes
2 answers
135 views

First EXPERIMENTAL proof of indistinguishability of electrons

Fairly early on in Thermodynamics there was a suggestion that particles are generally indistinguishable because of entropy paradoxes. Later on, my recollection is that somebody in the 1920's shot ...
Ernie's user avatar
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8 votes
1 answer
459 views

Entropy of mixing identical gases

I think this is called Gibbs paradox, but I am having some trouble understanding intuitively the entropy of mixing two identical gases in two volumes. It is said that after we remove the divider ...
reesespieces's user avatar
0 votes
3 answers
196 views

Bosonic Gas vs Ideal Gas

Bosonic Gases and Ideal Gases have these properties in common: They are composed of indistinguishable particles. The particles of both gases do not obey the Pauli Exclusion Principle. As far as I ...
user avatar
2 votes
4 answers
477 views

Why doesn't the Pauli exclusion principle apply to bosons?

Everything I've read online seems to say/imply that the Pauli exclusions principle only applies to fermions and not bosons. As I understand it the Pauli exclusion principle arises when the spatial ...
kelfic42's user avatar
2 votes
1 answer
116 views

How do you correct a partition function to account for indistinguishability of particles in general?

Consider a container of ideal gas divided in half by a partition where each half is at the same temperature, pressure, volume, and number of moles. In my statistical mechanics class we have gone over ...
Adrian's user avatar
  • 393
0 votes
1 answer
71 views

How is it possible for 4 distinguishable particles that the particle with the largest mass occupies the first excited state?

In the system of 4 distinguishable particles. How is it possible that the more massive particle went into the first excited states while the rest of the particles remained in their ground states?DO ...
Memoona Mehmood's user avatar
2 votes
3 answers
247 views

Evidence for indistinguishable particles

What's the simplest evidence for indistinguishable particles? Is there any evidence/experiment without resorting to large ensemble/statistical results?
Mat's user avatar
  • 201
0 votes
0 answers
188 views

Identical Particles Combinatorial approach Wave function (anti)symmetrization

We are given five idential spin-half particles in Linear Isotropic Harmonic Oscillator potential. It is required to find the degeneracy of the ground state of the system. I understood the approach ...
curious_mind's user avatar
1 vote
1 answer
129 views

Giving arguments why indistinguishability is removed for high $T$ or low occupation nr. of an energy level (ideal quantum gas)

The average occupation nr. of an energy level in a bosonic/fermonic gas is: $$\langle n_i \rangle=\frac{1}{e^{\beta(\epsilon_i-\mu)}\pm 1}.$$ If we make the assumption that we have a quantum gas of ...
imbAF's user avatar
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0 answers
58 views

What is a quasi-photon (⁠•⁠ ⁠▽⁠ ⁠•⁠;⁠)?

Regarding the question- Do quasiphotons have mass? Could someone explain to me what a quasi-photon is in layman's terms?
user avatar
1 vote
1 answer
109 views

Why use branching rules for $SU(n)$ when classifying states in quantum many-body systems, rather than $GL(n)$?

I'm reading Group Theory and its Application to Physical Problems by Hamermesh, and am struggling to understand chapter 11, which is on classifying states of quantum many-body systems, mostly using ...
roymend's user avatar
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1 vote
0 answers
45 views

Annihilation of two-particles intermediate states

I'm doing time-independent perturbation theory at the fourth order to calculate dispersion energy of two-polarizable neutral atoms in their ground state and in the electromagnetic field vacuum, to ...
Rob Tan's user avatar
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1 vote
1 answer
116 views

How does the following definition of contruction/destruction operators for the Fock state of Fermions account for the anti-symmetrization?

Consider the following definitions of the creation and destruction operators for a Fermionic Fock state: $$\hat a^{\dagger}_n \left|N_0 N_1...\right.\rangle = (-1)^{\sum_{k<n}N_k}(1-N_n) \left|N_0 ...
IAmOneWithTheScientist's user avatar
2 votes
2 answers
223 views

Do solutions of the Schrödinger equation for multiple particles automatically obey spin-statistics?

Consider the Hamilitonian for a general two-electron system subject to an external potential $V_\mathrm{ext}$ and an interaction potential $V_\mathrm{ee}$. In this case $$H\psi(x, y) = -\frac{1}{2} \...
Dominic Shillingford's user avatar
1 vote
2 answers
157 views

Argument about identical particles

I am reading Schwartz, Quantum field theory and the standard model, p.207, 12.1 Identical Particles and some question arises (I think that I am beginner for quantum field theory and please understand):...
Plantation's user avatar
9 votes
7 answers
3k views

Struggling to understand Identical particles

I'm struggling with the concept of identical particles in QM. Say I have two electrons, with one trapped on my left $\left|\uparrow\right\rangle_1$ and one trapped on my right $\left|\downarrow\right\...
Kim Dong's user avatar
  • 700
1 vote
1 answer
296 views

Why is the degeneracy factor for Bose Einstein distribution set to 1 automatically?

In https://scholar.harvard.edu/files/schwartz/files/12-bec.pdf, the article says "With Bose-Einstein statistics, we determined that using the grand canonical ensemble the expected number of ...
Larry's user avatar
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1 vote
0 answers
86 views

Increase of entropy when mixing two gases [duplicate]

I was reading my textbook and ran into this case: two ideal gases in a container are initially separated by a wall, with the same volume, the same amount (in moles), the same temperature, and the same ...
Michael's user avatar
  • 129
0 votes
2 answers
312 views

Wavefunction for multi-particle systems

As described in the photo(the explanation is given below Equation 11.1.2) we always have one wave function for many-particle systems as well. Then the author describes how an attempt to have the ...
The Theory's user avatar
2 votes
1 answer
221 views

On the definition of the bosonic one-particle reduced density matrix

Consider the bosonic/fermionic Fock space $F^\pm:=\bigoplus\limits_{N=0}^\infty H_N^{\pm}$, where $H^+_N:=\vee^N \mathfrak h$ and $H^-_N:=\wedge^N \mathfrak h$ for some (complex, separable) one-...
Tobias Fünke's user avatar

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