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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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Spin-1 particle as a bound state of two particles - how to write state ket?

Consider a spin-1 particle that is a bound state of two particles of spin-1/2. How do you write the state $\left|\alpha\right\rangle$ if the two particles are distinguishable? the two ...
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1answer
338 views

Identical particles and antisymmetric wavefunction

I am just confused about why the overall wavefunction of two identical particles should be antisymmetric. I was looking at this lecture note from University of Edinburgh's QM course: So the way ...
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1answer
139 views

Two identical particles

A system made up of two spin-$1/2$ identical particles is prepared such that: a measurement of $\mathbf{L}_{1}^2$ and $\mathbf{L}_{2}^2$ gives $2\hbar^2$ with certainty; a measurement of $...
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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. ...
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1answer
102 views

How can two photons with different frequencies created by parametric down conversion be indistinguishable? [closed]

We have two photons created by the same four wave mixing process. How are they indistinguishable if they have different wavelengths? I know that as they are created at the same moment by the same ...
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4answers
725 views

For ideal classical gasses, in terms of the energy levels why do we ignore whether the particles are fermions or bosons?

I am confused as to why when dealing with ideal classical gasses, the dependency of the particles being either fermions or bosons is ignored. How does this relate to the energy levels within the ...
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1answer
358 views

Identical particles: why a symetric or antisymmetric wave function?

I've read in many text books that the indistinguishability of two identical particles at $x$ and $y$ implies: $$|\psi(x,y)|=|\psi(y,x)|\quad (1)$$ This sounds rather natural. Then they say there ...
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2answers
629 views

What is the wavefunction of a system consists of both Fermions and Bosons?

Under the exchange of particle, the state of Fermions and Bosons are anti symmetric and symmetric respectively. For example, if $\psi_1(x)$ and $\psi_2(x)$ are two one particle wavefunctions, two ...
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1answer
97 views

Ideal Gas: an unexpected consequence of indistinguishability and the $N!$ term

I came across an issue which bugs me. Considering an ideal gas of $N$ non-interacting particles on a $1D$ container of length $L$, its (configurational) entropy $S$ reads $$ S = kT \ln \Big(\frac{L^...
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2answers
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What is special about the indistinguishability of Boson and Fermions?

In the treatment of Bosonic or Fermionic systems that I'm familiar with, you start with a state containing at least two particles: $$ \left| a_{i}, a_{j} \right\rangle $$ And define a permutation ...
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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 ...
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1answer
122 views

Why can a coupled wavefunction of 2 nucleons seemingly arbitrarily give two different expressions?

When looking at the Isospin representation of a proton-neutron system (with the notation $|I,I_3\rangle$), you can go from an uncoupled to a coupled representation like this: $$\textstyle|\frac{1}{2},...
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1answer
577 views

(How) Can the permutation operator be applied to wave functions?

The permutation operator $\hat{P}_{xyz}$, for a system of three particles, assigns the quantum numbers of particle 1 to particle $x$, of particle 2 to particle $y$ and so on. That is, given a ket, e.g....
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2answers
88 views

How to distinguish different electrons?

Suppose in the system of two electrons, can you use the electron spin to distinguish the electrons. In the whole system of particles,where the electrons are swapped,the quantum state of the system ...
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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
103 views

Does entropy really not increase here?

Two vessels separated by a partition have equal volume $V_0$ and equal temperature $T_0$. They both contain the same ideal gas, and the particles are indistinguishable. The left vessel has pressure $...
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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 ...
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5answers
183 views

Why do the laws of quantum mechanics not allow to put a pile of fermions all at a same place?

While i was reading the book "THE PARTICLE AT THE END OF UNIVERSE", the author said that we can not place a of pile fermions in a same place because laws of quantum mechanics do not allow that. ...
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3answers
193 views

Does Pauli Exclusion forbid two neutral fermions to occupy the same location in space?

I know that the Pauli Exclusion Principle does not allow two identical fermions to have the same set of quantum numbers. But can they share the same location in space if they are uncharged such as two ...
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3answers
743 views

Symmetric Under Particle Exchange?

Usually, in undergrad QM, we see states such as: $$|\psi\rangle_{\pm}=\frac{1}{\sqrt 2}(|01\rangle\pm|10\rangle)$$ Where trivially the + state is symmetric, and the $-$ state is antisymmetric. However,...
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1answer
133 views

Why does a quantum gas lose its “quantum nature” in the limit $(\epsilon-\mu)/k_BT\gg1$?

Mathematically, the Fermi-Dirac (FD) distribution and Bose-Einstein (BE) distribution coincides with the Maxwell-Boltzmann (MB) distribution in the limit $(\epsilon-\mu)/k_BT\gg 1$. Therefore, in this ...
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1answer
78 views

What do we mean by “particles” when talking about identical particles in QM?

A molecule of O$_2$ and a molecule of my DNA are not identical. Therefore, some sort of restriction must be placed on the word "particle", but what sort of restrictions and why them, not others? ...
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Identical particles seem to reduce probability

$\newcommand{\ket}[1]{| #1\rangle}$This question basically has two very related parts. This came up in the context of trying to verify something my professor said a while ago: that if the wave ...
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2answers
67 views

Can we talk about two atoms interchanging electrons?

I saw a discussion on this on Reddit so I thought I'd ask here to get a more authoritative answer. Say you have two atoms, separated so that the electron wavefunctions have negligible overlap. ...
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2answers
864 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 ...
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1answer
472 views

Finding states of a system of 2 identical bosons (including spin)

I'm trying to find the ground state and first excited state for 2 identical bosons in an infinite square well. I know that both states are degenerate and the spatial and spin parts of the wave ...
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1answer
508 views

Help understanding two identical particles with spin

I'm trying to understand the wave function of two identical particles with spin but unfortunately my textbook does a poor job explaining any of it. For two identical bosons, for instance, I know that ...
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1answer
419 views

Quantum entanglement for indistinguishable particles

When I encounter the definition of the mathematical definition of quantum entanglement. System composed by many parts $A$, $B$,.., $N$ can be described by a density matrix operator $\hat{\rho}$ acting ...
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1answer
203 views

Understanding concepts of $N$ identical particles

I'm uncomfortable with the concepts of $N$ number of identical fermions and identical bosons and their degeneracies and energies. For example, lets say we a have a 3-dimensional isotropic harmonic ...
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1answer
1k views

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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1answer
600 views

Finding the symmetry of electron spin and position states using Clebsch-Gordon tables?

I know that spin and position states must be symmetric and antisymmetric (and vice versa), but I can't figure out how to use Clebsch-Gordon Tables to figure out the symmetry of either one. For ...
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1answer
80 views

Are all nuclei of a given isotope of a given element necessarily identical?

Consider two nuclei with exactly P protons and N neutrons each. Is it possible for their nuclei to be different? (e.g., for the "clouds" to be distributed differently?) By "different" I mean that e.g. ...
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1answer
48 views

Is distinguishability based on the empirical fact of the distribution or is the distribution derived from distinguishability?

If two particles are indistinguishable why do we call them two or is indistinguishability just code for "count the two distinct particles together - not as two - when counting what is equilikely and ...
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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]...
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1k views

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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2answers
723 views

Pauli matrix for triplet state?

Question is, what would be the result of applying the operator $\hat A = [3I + \vec\sigma_1 . \vec\sigma_2]$ on the |singlet$\rangle$ and |triplet$\rangle$ states ($\vec\sigma_1$ acts on the 1st ...
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2answers
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Why are He-4 nuclei considered bosons, and He-3 nuclei considered fermions?

Why are helium-4 nuclei considered bosons, while helium-3 nuclei are considered fermions? From the Wikipedia page on Identical Particles: Examples of bosons are photons, gluons, phonons, helium-4 ...
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143 views

Isospin and indistinguishable particles

I am trying to understand the properties of a proton-neutron system assuming that isospin is a good symmetry, so I will forget about electromagnetism, weak interactions, QCD and all those more ...
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74 views

Identical Particles in Non Relativistic Theory

I have a problem with the following reasoning taken from Messiah which is meant to show that there are intrinsic difficulties in identical particles which are neither bosons nor fermions. Suppose the ...
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1answer
162 views

Origin of Fermi-Dirac distribution?

I wanted to know what "problem" Fermi and Dirac wanted to solve with the Fermi-Dirac distribution in 1926? What was the context? What is the history behind this distribution? I hope the question is ...
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2answers
933 views

Partition function for classical indistinguishable particles and Bose particles

We have two particles that can be in either level $E_0 = 0$ or in level $E_1$. If we treat them as Bose particles, then the partition function will be: $$ Z = 1 + e^{-\beta E_1} + e^{-2\beta E_1}, $$ ...
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406 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 ...
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1answer
177 views

Quantum Field Theory is equivalent to QM of identical particles for free fields?

This question focuses on just free fields. The point is, studying Merzbacher's Quantum Mechanics book, in the chapter about identical particles, the author shows how Quantum Fields appear naturally ...
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1answer
211 views

Quantum: How do I find the degeneracy of 2 electrons in an infinite cube (3D) well? [closed]

There are two electrons inside an infinite potential cube well (essentially $V=\infty$ outside a cube and $0$ inside it) and I need to find the degeneracy of the first excited state. I'm thinking it ...
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0answers
216 views

Finding the state and wave-function for two identical spin-1 bosons trapped in one-dimensional harmonic oscillator

My question concerns the validity of my approach to a problem and wether the answer is correct. I am tasked with writing the state vector(s) and wave-function(s) for when two identical spin-1 bosons ...
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11answers
7k views

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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1answer
97 views

Identical particle exchange as a Yang-Mills theory

I am trying to find a quantum field theory (a Yang-Mills theory) for the identical particles exchange interaction. For a system of $N$ identical particles one has the state $|x_1,x_2,\ldots,x_N\rangle$...
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225 views

Interference with a minus sign

In Lectures on Physics, by Richard Feynman, pg 3-11, I found the following: In case of electrons, the interfering amplitudes for exchange interfere with a negative sign. I was unable to ...
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2answers
571 views

Two particles system

Source: this video For a system with two particles (09:30), why is its wave function a product of each particle's wave function? E.g. $$\psi(x_1,x_2)=\psi_a(x_1)\psi_b(x_2)$$ For indistinguishable ...
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1answer
444 views

How to understand permutations of particles in Quantum Mechanics?

I'm studying identical particles in Quantum Mechanics and I'm having a hard time to understand the idea of permutations of particles from a mathematical standpoint. From one intuitive point of view ...