Questions tagged [identical-particles]

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

163 questions
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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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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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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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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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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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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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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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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

$\newcommand{\ket}{| #1\rangle}$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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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 ...