# Questions tagged [identical-particles]

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

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### Creating multiparticle states from vacuum in QFT

In creating multiparticle states from the vacuum we apply the creation operators, \begin{align} &|p_1,s_1\rangle=a^{\dagger}_{p_1,s_1}|0\rangle,\\ &|p_1,s_1;p_2,s_2\rangle=a^{\dagger}_{p_1,s_1}...
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### What exactly does an exchange of particle labels for identical particle wave functions mean *physically*?

We know that the wavefunction of identical particles behaves as follows: $$\Psi(1,2)=\begin{cases}-\Psi(2,1) & \text{for fermions} \\ +\Psi(2,1) & \text{for bosons} \end{cases}$$ Now, what ...
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### $N$ bosons in two energy levels

What is the partition function for $N$ bosons in a two state system with $E_1=0$ and $E_2= E$? I know that bosons don't obey the Pauli exclusion principle and they are indistinguishable but I am ...
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### General counting of microstates for a specific energy. Indistinguishable vs distinguishable

I have the following problem: I have two systems $A$ and $B$, each one with 5 distinguishable particles, $N_A=N_B=5$. The systems have infinite energy levels with energy $E_m = m \cdot \epsilon$ with ...
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### Exchange symmetry between mixed species

I am reading Weinberg Vol.1 chapter 4, in section 4.1 page 171 last paragraph he says that for interchanges of particles to different species can be taken to be symmetric for any two bosons or one ...
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### Why must systems of identical particles be either totally antisymmetric or totally symmetric? Why can there not exist a mixture?

I am reading chapter 6 of Sakurai's Modern Quantum Mechanics and have come across the 'symmetrization postulate', which tells me that for any given system of identical particles, all states must ...
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### Identicalness and Indistinguishability in quantum mechanics

I've been reading chapter 10.3 'Identical Particles' in Shankar's book on quantum mechanics and also looked through some of other books on this subject and one rather subtle objection started ...
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### Problem regarding Eigenfunctions of Identical Particles in Quantum Physics

Suppose I have 2 electrons under an harmonic potential: $$H=\frac{1}{2m}(p_1^2+p_2^2)+\frac{1}{2}m\omega ^2 (x_1^2+x_2^2)$$ Now let's think about the eigenvalue and the eigenfunctions of energy of the ...
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### Slater determinant as (zero order) approximation to Schrodinger equation

I understand how the Slater determinant for N particle works and its application in writing an antisymmetric wavefunction. However the question asks me to show that the Slater determinant is a zero ...
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### Motivation behind the principle that all electrons are not distinguishable

EDIT: It is usually claimed without providing much motivation that elementary particles of the same kind, e.g. electrons, are not distinguishable in principle: there is no way to distinguish between ...
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### Properly accounting for indistinguishability of (homonuclear) diatomic molecules in “internal” partition function

I have always liked Schroeder's take on the partition function being a product of translational and internal degrees of freedom: $$Z_1 = Z_{\text {trans}} Z_{\text{int}}$$ where $Z_{\text{int}}$ can ...
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### Confused about partition function of identical particles

The total partition function of N identical, independent particles is $Z^N/N!$ where Z is the partition function of a single particle. To find out the correct magnetization due to N identical atoms of ...
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### Making indistinguishable particles distinguishable 2.0

An extended discussion of the selected best answer to the following SE question. In part 2 of the answer concerning 'far-apart' particles, I don't see how the equality can follow in the first integral....
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### Permutation of Identical Fermions - Spatial and Spin Decomposition

As far as I know, fermions are the particles which exhibit antisymmetric states: $\hat{P}\left|n_1\right>\otimes\left|n_2\right> = -\left|n_2\right>\otimes\left|n_1\right>$. Often times, ...
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### Spin wave function of two identical spin-1/2 particles in a 1D potential box

I came across this problem in N. Zettili's Quantum Mechanics book (Chapter 9, Problem 16): Two identical particles of spin 1/2 are enclosed in a one-dimensional box potential of length L with walls ...
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### Why is every electron in the universe not entangled with every other electron?

According to the principles of identical particles, the wavefunction of a collection of fermions must be antisymmetric and such a state is entangled. Doesn't this mean that any given electron in the ...
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### Why are all quarks and leptons of this universe the same?

We know the composition of stars by spectroscopic analysis. The EM waves generated by them are blue- or redshifted. We could have said, "Look, the wavelength is slightly different so it may be ...