Questions tagged [identical-particles]

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

Filter by
Sorted by
Tagged with
0 votes
1 answer
39 views

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
  • 581
4 votes
1 answer
759 views

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
  • 2,276
0 votes
0 answers
22 views

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
3 votes
0 answers
62 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
0 votes
0 answers
28 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
  • 1
1 vote
1 answer
99 views

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
70 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
  • 83
0 votes
0 answers
23 views

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
  • 1
5 votes
2 answers
515 views

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
50 views

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
  • 117
0 votes
1 answer
101 views

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
  • 3
2 votes
1 answer
108 views

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
0 votes
1 answer
132 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
  • 361
2 votes
1 answer
365 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
  • 51
1 vote
1 answer
53 views

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
  • 99
0 votes
6 answers
264 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
  • 883
1 vote
1 answer
234 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
  • 149
1 vote
1 answer
66 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
  • 2,423
0 votes
0 answers
54 views

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
128 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
  • 49
8 votes
1 answer
430 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
153 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
0 votes
0 answers
29 views

Dependence of phase factor when interchanging two identical particles on spin

In Weinberg's textbook on QFT (page 171), he discussed the phase $\alpha_n$ picked up when interchanging two identical particles. Generally, the phase may depend on the spin of two particles ...
Eric Yang's user avatar
  • 1,046
2 votes
4 answers
365 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
107 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
63 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
198 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
  • 148
0 votes
0 answers
159 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
120 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
  • 1,322
0 votes
0 answers
53 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
102 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
  • 780
1 vote
0 answers
39 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
  • 864
1 vote
1 answer
111 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
187 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
0 answers
72 views

Problem on identical particles [closed]

Question : Two identical particles are described by the hamiltonian $$H=\frac{p_1^2(x_1)}{2m}+\frac{p_2^2(x_2)}{2m}+\frac{m\omega^2x_1^2}{2}+\frac{m\omega^2x_2^2}{2}$$ Obtain the energy spectrum of ...
user231188's user avatar
1 vote
2 answers
144 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
  • 666
1 vote
1 answer
223 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
  • 137
1 vote
0 answers
83 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
  • 119
0 votes
2 answers
230 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
1 vote
0 answers
167 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
4 votes
0 answers
114 views

Why, conceptually, are identical bosons "pulled together" and identical fermions "pushed away"?

I have seen the calculation for the separation distance of indistinguishable particles versus distinguishable ones. According to Griffiths (Pg. 204 3rd Ed.), the difference in separation distance is $$...
Relativisticcucumber's user avatar
0 votes
0 answers
64 views

Is there an additional value carried by fundamental particles (like spin for example) that acts like an ID?

My question arose after reading this: https://www.npr.org/sections/thesalt/2019/11/03/772030934/soups-on-and-on-thai-beef-noodle-brew-has-been-simmering-for-45-years Synopsis: In perpetual stew they ...
Jack Hulse's user avatar
1 vote
1 answer
46 views

System of two noninteracting, unentangled electrons: spelling out the state

Let's say we have a spin-up electron near x=-10: $$\psi_1 = |\uparrow\rangle\alpha(x_1)$$ $\alpha$ being the space part: a bump near x=-10. Similarly we have a second spin-down electron near x=+10: $$\...
Travis Lee's user avatar
0 votes
1 answer
112 views

Completeness Relation With Identical Particles

I came across something that is bugging me regarding the completeness relation. This identity states the following $$ \sum_{\mu} | \mu \rangle \langle \mu | = 1, $$ and with identical particles, this ...
Rich Hard Fine Man's user avatar
0 votes
1 answer
93 views

Identical particles far apart

There are two identical particles, $a$ and $b$. The particle distance is large enough that interaction term, in the Hamiltonian, is negligible. The Hamiltonian of the system can be written as: $$\hat ...
SimoBartz's user avatar
  • 1,770
1 vote
1 answer
168 views

Symmetry of the total spin eigenstate for systems of three and more identical particles

I have just found very nice question and answer: How to determine whether an eigenstate of total spin is symmetric or antisymmetric? concering the relation of the value of the total spin and the ...
drer's user avatar
  • 296
0 votes
0 answers
85 views

Interpretation of the excitations of the Klein-Gordon Field

Having quantized the Klein- Gordon field and having described the respective hamiltonian in terms of creation and annihilation operators, one finds that eqn 2.49 (in the photo) is satisfied(because of ...
Cbb Ttt's user avatar
  • 70
1 vote
1 answer
152 views

Physical interpretation of the Pauli Exclusion Principle

As I understand it, the Pauli Exclusion principle states that two electrons in orbitals of a given atom with the same values for quantum numbers $n$, $l$ and $m_j$ must have different (opposite) ...
slithy_tove's user avatar
1 vote
2 answers
105 views

Multi-particles system wave function

As we all know there is a symmetric and antisymmetric of 2 particles system states. \begin{align} \text{symmetric} & \ \rightarrow & |μ,ν⟩=\frac{|μ⟩|ν⟩+|ν⟩|μ⟩}{\sqrt{2}} \\ \text{antisymmetric}...
DDonkey's user avatar
  • 41

1
2 3 4 5
8