Questions tagged [identical-particles]

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

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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 ...
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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 ...
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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} \...
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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 ...
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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):...
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Degeneracy of three identical electrons [duplicate]

I was studing identical particles from the Zettili and Griffiths book, and i have a question about the possible states and the degeneracy. In Zettili solved problem 8.1 (item c) and Griffiths problem ...
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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\...
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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 ...
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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 ...
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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 ...
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Is the definition of the bosonic one-particle reduced density matrix well-defined?

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-...
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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 $$...
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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 ...
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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: $$\...
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Wavefunction collapse of Identical two particle system- What does following wavefunction tell us?

What is this equation telling us? $\psi_a$ and $\psi_b$ are the wave functions of particle 1 and 2 respectively; and $r_1$ and $r_2$ are position vectors of particle 1 and particle 2 respectively. \...
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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 ...
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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 ...
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Integral in self-consistent field method

Suppose we have $n-$ electron system. So, $$\psi^{(N)}=\frac{1}{\sqrt N!}\sum_{P=1}^{N!}(-1)^PP{\{u_{\alpha_1}(q_1),u_{\alpha_1}(q_1),...,u_{\alpha_1}(q_1)}\}.$$ Consider operator $\Omega=\sum_{i=1}^...
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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 ...
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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 ...
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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) ...
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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}...
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Do the parts of proton move around and in that sense all protons, unlike electrons, are not the same? [duplicate]

Two different protons could be in a different state because of its parts "moving" in some sense?
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To what extent Dirac sea is accurate to model fermion systems?

This question is related to an answer from the Matter Modeling stack exchange How spin-orbit coupling makes spin-forbidden reactions possible?. The situation changes when the full Dirac equation is ...
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Does "non-interacting" (fermions) really mean "no interactions other than Pauli exclusion"?

When one speaks of non-interacting elections (or other ferimons), doesn't one technically mean non-interacting but with the exception of Pauli exclusion? I wonder if it is appropriate to view Pauli ...
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Formalism to go from distinguishable to indistinguishable states in quantum mechanics, and the probability combination rules?

I was wondering how can we go from an analyzed system of particles, where we have considered them to be distinguishable, to results about the same particles where we consider them indistinguishable. ...
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Is the NOON state entangled even if $N=1$?

Let $\mathcal{H}\cong\mathbb{C}^2$ be the Hilbert space of states of a single particle. Let $\{|\psi_A\rangle, \psi_B\rangle\}$ be a basis for $\mathcal{H}$. I now want to describe an ensemble of ...
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Two identical output particles in decay and scattering process in quantum field theory

I am troubled for if we need to divide the factor of $2$ for two identical output states in decay and scattering process in quantum field theory. Consider Peskin and Schroeder's QFT book, on page 127, ...
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Contraction with external legs in $S$-matrix

If we consider following $S-$matrix element:$$\left\langle\mathbf{p}_1 \mathbf{k}_2|T\{\phi(x_1) \phi(x_2)\}| 0\right\rangle_0 $$ where $\phi$ denote Klein-Gordon field, and apply the convention in ...
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Cross Section Formula

This relates to page 74 of Timo Weigand's QFT notes. Specifically 2.170: $$\omega_{fi}=\frac{1}{N!}\left[ \prod_{n=1}^N \int \frac{d^3k_n}{(2\pi)^3}\frac{1}{2E_n}\right] (2\pi)^4 \delta^{(4)}\left(\...
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How does pilot wave theory explain "identical particle" interference?

Pilot wave theory says that there exist waves in 3D space which carry particles. This explains, say, the double slit experiment. But this does not explain the behavior of identical particles. ...
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Continuous motion is a myth and the speed of light is a convention [closed]

Suppose that we have two particles, $A$ and $B$, which are identical in all respects except for their positions, and position-dependent properties (velocity, momentum, etc.) At some point in time, ...
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Is Pauli's Exclusion Principle a restatement of what experiments have shown?

So were studying the configuration of electrons in an atom and one thing that popped up was Pauli's Exclusion Principle. In our class, as well as our textbook, it was stated as the fact that two ...
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Slater determinant of three fermions without spin

The Slater determinant takes into account the Pauli principle, but if the fermions have no spin, a degree of freedom is missing. What would the determinant look like then?
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Eigenvalues of Exchange Operator

$\hat P$ is the exchange operator, the standard derivation of its eigenvalues, $\pm 1$, takes advantage of the fact that exchanging the particles two times changes nothing. Mathematically: $$\hat P \...
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Are chemical Isomers identical particles?

I confused that if different isomers are identical particles or not? If yes, how about $^4$He and D$_2$ (these two are not isomers but contain the same number of protons, neutrons and electrons)? If ...
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Identical Particles in QM

In Shankar's QM book pg. 261, he said that in classical mechanics we can distinguish between identical particles by observing their histories (or previous trajectories), which are non-identical. Why ...
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Confusion with Pathria's derivation of the Canonical Ensemble

I've some problems understanding Pathria's derivation of the canonical ensemble and the probability of a system being in a certain state. According to Pathria ( section 3.2 ), we consider an ensemble ...
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Can the "symmetric & antisymmetric" stuff of fermions & bosons be explained by first principles? [duplicate]

Many particle wave-functions to me have a very confusing methodology. I've been taught some procedure for creating wave functions that are symmetric or anti-symmetric upon exchange of coordinates. I ...
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Are photons with different frequency distinguishable?

When i learn statistical mechanic, the teacher told me that photons with different frequency are distinguishable, i confused. And the teacher say also photons with different polarization, direction ...
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Identical particles in Bohmian quantum mechanics

Particles can be distinguished by their trajectories in Bohmian quantum mechanics and there is no natural reason for imposing symmetrization (or anti-symmetrization) of the wave function of the ...
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Mixing identical gases in different states (Gibbs paradox)

Background It is well known that if we take a container separated into two volumes $V_1$ and $V_2$ by an insulating membrane and containing some moles $n_1$ and $n_2$ of the same gas at the same ...
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Question regarding the degeneracy of energy states of Fermions

My professor during the lecture said exactly the following Let there be a system of non-interacting fermions. Since they are indistinguishable, they have the same Hamiltonian, and the single-particle ...
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Partition function for the indistinguishable particles using symmetrization of states

In the derivation of the partition function for the the N particle ideal gas, the factor of $\frac{1}{N!}$ does not come naturally. We have to go for symmetrized and asymmetrized state. So, to derive ...
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Conservation of symmetrization in quantum mechanics

I recently read about the symmetrization requirement, which my book states is axiomatic of quantum mechanics: $$ \psi(\mathbf r_1, \mathbf r_2) = \pm \psi(\mathbf r_2, \mathbf r_1). \tag{*} $$ It ...
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Derivation of partition function for $N$ identical quantum harmonic oscillators

What is the partition function $$\mathcal Z^{(N)}_\beta(H) : =\mathrm{Tr}\exp(-\beta H) \tag{Z} $$ $\left(\beta >0\right)$ for a system of $N$ indistinguishable and non-interacting bosons (e.g. ...
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2 fermions in a box (infinite potential well)

I have 2 fermions in a box. I know that they are in the state: $$|\psi\rangle = {1 \over \sqrt2}\, (|1\rangle |2\rangle -|2\rangle|1\rangle)\,|+,+\rangle$$ If I hadn't spin, I could find wave ...
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Partition Function quantum identical particles

In Pathria and Beale Statistical Mechanics section 5.5, the book tries to compute the Partition function of a system of noninteracting, indistinguishable particles confined to a cubical box of volume $...
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Is there a relation between the density matrix and the density of the position probability? Are they the same concept?

We have a system of two bosons particles and we are interested in calculating the one-particle density and two-particle-density when both are in different states. So, to do that, I consider the ...
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What if we charge an uncharged sphere by making contact with sphere bearing 3 electrons charge

Suppose say we have 2 identical conducting spheres. Then we have removed 3 electrons from one of the sphere. Now how will charge distribute on each sphere after charging the uncharged sphere by ...
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