Questions tagged [identical-particles]
Questions related to the discernibility of many-body systems, its philosophical implications and its mathematical description.
262
questions
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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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1answer
43 views
Factor of 1/2 in the cross section of Møller scattering
I have seen everywhere (like Wikipedia) that in
Møller scattering the cross section is calculated with the formula:
$$\frac{\mathrm d \sigma}{\mathrm d \Omega} = \frac{1}{64 \pi^2 E_{CM}^2 } \frac{|\...
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4answers
59 views
Momentum and photon indistinguishability
Suppose two photons have the same frequency and polarization, and their wavepackets also have identical temporal and spatial (along their propagation directions, respectively) profiles.
The two ...
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1answer
35 views
Degeneracy in $N$-particle Quantum System [closed]
I was recently introduced to the concept of $N$ particle systems in Quantum Mechanics, and the concept of indistinguishable and distinguishable particles. While reading the following material online, ...
1
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1answer
55 views
Normalization of Slater Determinant and Antisymmetry
Consider a system consisting of two electrons with Slater-Determinant $\vert\chi_1\chi_2\rangle$, where $\chi_1$ and $\chi_2$ are one-electron orbitals (spin-orbitals). The Slater Determinant is ...
0
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1answer
33 views
When is it necessary to use more than one Slater determinant to write the wave function of a quantum system?
Consider a system of $N$ non-interacting identical fermions of spin $s$, spin quantum number $m_i=m_{s_i}$and position coordinates $\mathbf{r}_i$. Let $\alpha$ denote a state specified by the numbers $...
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0answers
36 views
Quantum Mechanics - Prove that the permutation operators do not commute in general
Previously, in my Quantum Mechanics exam,
We have asked to "Prove that the permutation operators do not commute in general."
And I have answered it as follows
But my teacher marked it as ...
1
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1answer
32 views
Identical particles placed on the energy levels of a 1D harmonic oscillator
If the particles are 6 spinless bosons, would they tend to occupy the ground state together and make the lowest total energy of the system $E=6E_0=3 \hbar \omega$?
And If the particles are 6 spin 1/2 ...
1
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1answer
104 views
Adding quantum numbers breaks exclusion principle?
Consider 2 non-interacting Fermions with spin $s\ne 0$ trapped in a 1D harmonic potential with ground state $\left|\phi_0\right\rangle$. Due the Pauli exclusion principle I would expect that only 1 ...
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2answers
86 views
Indistinguishability in statistical mechanics
I have two questions about using the concept of indistinguishability to determine the partition function in statistical mechanics, like for instance when determining the partition function of an ideal ...
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2answers
45 views
Identical particles
I am reading Quantum Mechanics from Griffiths (for the first time); in chapter 5 (2nd ed.) page-179 it is written:
Now I really is not able to understand what Griffiths exactly wants to say by the ...
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2answers
37 views
Finding the number density of a Fermi gas
When calculating the number density of a Fermi-Dirac or Bose-Einstein distributed particle:
$$n=\frac{g}{2\pi^3} \int f(\vec{p})d^3p$$
Apparently one can change variables and get
$$n=\frac{g}{2\pi^3} \...
2
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2answers
101 views
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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1answer
159 views
$N$ 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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1answer
32 views
In thermodynamic limit, how is $\frac{V}{(2 \pi)^{3}} \int \mathrm{d}^{3} k= \int \frac{\mathrm{d}^{3} r \mathrm{~d}^{3} \boldsymbol{P}}{h^{3}}$?
In the book Intro. Statistical Physics by K.Huang, on page 106, it is given that
Because of indistinguishability; the $N$ -body wave function is labelled by the set $\left\{\alpha_{1}, \cdots, \...
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1answer
34 views
Ground state energy for fermions with different spin orientation [closed]
Electrons are subject to a harmonic potential in one dimension, described by one-particle Hamiltonian $$H = \frac{P^2}{2m}+\frac{1}{2}m\omega X^2,$$ where $P$ are the momentum operator, $X$, is the ...
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2answers
74 views
Partition function
I am trying to calculate the partition function of a system that has 2 bosons (spin 0) in thermal equilibrium with a reservoir. The particles are independent and each one admits as possible orbitals ...
0
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1answer
122 views
Question about the Partition Function For 2 Fermions In a 2-Level System
So say we have $2$ indistinguishable electrons that can occupy $2$ energy states $E=0$ and $E=\Delta$. If we only had one fermion then are both states doubly degenerate since an electron can be spin ...
0
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1answer
51 views
Fermions and Pauli Exclusion Principle
I started to study quantum ideal gas and I am reading Salinas "Introduction to Statistical Physics". In chapter 8 , he states that when speaking of fermions, only one particle can occupy an ...
0
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1answer
55 views
Why is a 2-electron wavefunction antisymmetric? [closed]
Why does a 2-electron system have an antisymmetric wavefunction when the combination should be bosonic? I.e. If it's an overall bosonic combination, shouldn't the overall wavefunction be symmetric?
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2answers
75 views
Don't the four quantum numbers make two electrons distinguishable?
From the Pauli's Exclusion Principle no two electrons in a bound system have all same quantum numbers. This means that an electron can be uniquely specified by the four quantum numbers and hence can ...
2
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1answer
110 views
What happens when two 0-spin identical bosons interact?
Suppose we have a system of two identical 0-spin bosons, with a certain symmetric, time independent hamiltonian, which involves some general angular momentum for each particle (I am not currently ...
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5answers
228 views
Identical Particles in Quantum Mechanics
I'm reading Chapter 5 of Griffiths' Quantum Mechanics book about "Identical Particles". He says that:
The state of a two-particle system is a function of the
coordinates of particle one ($...
2
votes
1answer
53 views
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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0answers
30 views
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 ...
2
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1answer
75 views
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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3answers
133 views
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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3answers
66 views
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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0answers
65 views
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 ...
1
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2answers
88 views
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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1answer
32 views
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 ...
0
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1answer
71 views
Does this wave function violate any rules of Quantum mechanics?
I am studying bosons and fermions in quantum mechanics. We learned that for a two-particle system with identical bosons, the wave function can have the form (assume symmetric spin)
$$ \frac{1}{\sqrt2} ...
5
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4answers
578 views
Contradictory statements on product states for distinguishable particles in Quantum Mechanics
Page no. $5$ in Many-Body Theory Exposed! by Willem H Dickhoff & Dimitri Van Neck states the following:
The complex vector space, relevant for N particles, can be constructed as the direct ...
6
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2answers
311 views
Distinguishability and tagging of particles
I was reading Sakurai's book and here is an extract:
In classical physics it is possible to keep track of individual particles even though
they may look alike. When we have particle 1 and particle 2 ...
0
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1answer
33 views
Indistinguishability in Spin-1/2-system
In terms of statistical physics I thought the microcanonical partition function can be interpreted as summing over all possible quantum numbers. Neglecting indistinguishability in the case of two ...
5
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0answers
132 views
Different types of magnetic exchange
I am a bit confused about the mechanisms of different types of exchange. Mainly, I am trying to understand mechanisms that lead to magnetic ordering and I came across several different types of ...
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4answers
4k views
Does it make sense to ask how many of the molecules you are inhaling Caesar exhaled in his last breath?
There is a nice example of a Fermi estimation question where you ask: How many of the molecules which Julius Caesar (or Jesus, Muhammad, etc. - anyone who died a long time ago) exhaled in their dying ...
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1answer
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Interfering alternatives and identical particles in Feynman and Hibbs
I am currently self-studying Feynman and Hibbs, and in his first chapter, Feynman talked about 'alternatives' like the various possibilities or paths an experiment can take. He defined two different ...
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3answers
79 views
Can identical particles be “distinguished” by their states?
Let's say we have an atom with three electrons in the lowest energy states. So two electrons are at energy level 1 and one at energy level 2. Now we measure the positions of those electrons, and found ...
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1answer
29 views
Valid state of electron systems
I would like to show that the state $|\psi \rangle = |\varphi_1,\varphi_2,\varphi_3 \rangle$ is not a valid state for 3 electrons (without spin) for $|\varphi_1\rangle,|\varphi_2\rangle,|\varphi_3 \...
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0answers
30 views
Scattering of identical particles
I am studying scattering of identical particles using the book of Joachain and I am having some difficulties. Consider the scattering of an electron by an atom with $N$ bound electrons. The asymptotic ...
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0answers
42 views
Measuring a superposition state of identical particles
Suppose that the state of a system of two identcial particles (say, two photons) is given by the following:
$$\frac{1}{\sqrt{}2}(|\psi_{1}\rangle|\psi_{2}\rangle + |\psi_{2}\rangle|\psi_{1}\rangle) \, ...
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1answer
51 views
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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0answers
40 views
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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1answer
67 views
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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1answer
563 views
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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4answers
7k views
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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1answer
69 views
Identical Particles in Quantum Field Theory
In Quantum Field theory by M. Schwarz, the author in the introduction of chapter 12 on Spin Statistics theorem says, while describing identical Particles:
Let $$|s_1p_1n_1,...,s_3p_3n_3\rangle \tag{1}$...
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1answer
53 views
The Indistinguishability Postulate and the Copenhagen Interpretation
The indistinguishability postulate states that any (normalized) state vector $|\psi\rangle$ for a system of $N$ identical particles should satisfy $\langle \psi | \hat{O} | \psi \rangle = \langle \hat{...
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9answers
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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 ...
