Questions tagged [identical-particles]
Questions related to the discernibility of many-body systems, its philosophical implications and its mathematical description.
5
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1answer
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When is separating the total wavefunction into a space part and a spin part possible?
The total wavefunction of an electron $\psi(\vec{r},s)$ can always be written as $$\psi(\vec{r},s)=\phi(\vec{r})\zeta_{s,m_s}$$ where $\phi(\vec{r})$ is the space part and $\zeta_{s,m_s}$ is the spin ...
0
votes
1answer
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Partition Function of an Ideal Gas
Which is the correct partition function for an ideal (bosonic) gas at high $T$:
1) Sum over the number of particles in each momentum state:
$$ z_{\vec{p}} = 1 + e^{- \varepsilon_{\vec{p}}/T} + ... = ...
3
votes
5answers
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Spin of two identical particles
I read that when I have two identical particles with spin 1/2 there are 4 possibilities:
|↓↓⟩,|↑↑⟩,|↑↓⟩,|↓↑⟩.
Then since there is the symmetrization requirement I can take as eigenvalues the ...
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vote
2answers
63 views
What would happen if I put two identical particles close enough?
Is there a repulsive force between these two particles to prevent them from being in the same point? I mean, in order to obey Pauli exclusion principle?
2
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2answers
53 views
What is the simplest possible Hamiltonian that yields an Antisymmetric Wavefunction?
I am using a Split-Operator Fourier Transform (SOFT) technique to solve the time-dependent electronic Schrödinger Equation (TDSE) for a Hydrogen molecule under the Born-Oppenheimer approximation. So I ...
0
votes
1answer
78 views
Why is $\psi_{atom}=\psi_a\psi_b$ not a suitable wavefunction for the Helium atom?
In the approximation that the two electrons of the He atom moved independently of each other, we can say that electron 1 is in state $\psi_a(1)$ where $a$ represents the orbital quantum numbers $nlm$ ...
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0answers
41 views
Why particles should be indistinguishable in statistical mechanics when deriving Maxwell distribution? [duplicate]
When calculating the number of microstates in statistical mechanics, we assume that particles should be indistinguishable. What is the reason behind it?
0
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0answers
14 views
Can I distinguish a Bose-Einstein Condensate of composite bosons from one of elementary bosons?
The only requirement for an ensemble of particles to undergo a transition into a BEC is to be bosons.
But two fermions also make a bosons.
Are there physical, measureable implications of a BEC being ...
0
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0answers
24 views
Do anyonic statistics only arise from spatial degrees of freedom?
Elementary texts on quantum mechanics justify the existence of fermions and bosons using the simple argument that if we have a state of two indistinguishable particles $|a,b \rangle$, where $a$ and $b$...
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votes
2answers
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About the symmetric spatial part of a two-electron wavefunction: Can it be that $r_1= r_2$ less favoured than $|r_1-r_2|\neq 0$?
The two-electron wavefunction of the ground state of helium is
$$
\psi(r_1,r_2)=\phi_{1s}(r_1)\phi_{1s}(r_2)\otimes (|\uparrow_1\downarrow_2-\downarrow_2\uparrow_1\rangle)/\sqrt{2}
$$
where $\phi_{1s}...
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2answers
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Does quantum gases obey ideal gas equation $ PV= nRT$?
At extremely low temperature, does an ideal gas of bosons or fermions obey the ideal gas equation, $PV= nRT$?
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0answers
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Spectrum of two particles system hamiltonian
Consider the following hamiltonian describing a system of two identical spin 1/2 particles in one dimension:
$$H = H_1 +H_2 - \lambda \vec {s_1} . \vec {s_2}$$
Where $H_i$ is the Hamiltonian of an ...
0
votes
3answers
107 views
Wave function of a system of two identical fermions
In N. Zettili's 'Quantum Mechanics Concepts and Applications' [chapter 8, solved problem 8.3], we have to find wave function and ground state energy of a system having two identical fermions and in ...
1
vote
1answer
45 views
Is the spin-statistics theorem true for antifermions?
The spin-statistics theorem says that having a system of identical fermions, the total wavefunction is antisymmetric with respect to exchange of any two fermions.
My question is, does this hold for ...
0
votes
1answer
37 views
Identical Spin Fermions in the same orbital state: Finding total spin
Say we have two identical spin 3/2 particles in the same orbital state. What are the possible total spin?
I know that there is a simple formula for adding angular momenta, but this breaks down when ...
1
vote
2answers
57 views
Indistinguishable particles and symmetrization of wavefunction
For 2 indistinguishable particles, we take the wave function to be
$$\psi\pm (r_1,r_2) = A[\psi_a (r1)\psi_b (r2) \pm \psi_b (r1)\psi_a (r2) ]$$
where fermions get a - sign and bosons get a +
But, if ...
2
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1answer
38 views
Configuration space of identical particles - fractional statistics
In Khare's book of fractional statistics and quantum theory, when discussing why we need fractional statistics he arrives at the configuration space
for a system of two identical particles in $d$ ...
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0answers
31 views
Indistinguishable particles and statistical mechanincs
i'm studying the paragraph 5.5 (page 119) of this book:
http://sciold.ui.ac.ir/~sjalali/MSc.Students/statistical.mechanics/pathria.pdf
Now at page 121 we have:
$$ \sum\limits_{p} \delta_p{u_{k1}}(...
2
votes
4answers
201 views
The wave function of a system of two identical particles
For a system of two identical particles, where $r_1$ is the position vector of particle 1 and $r_2$ is the position vec. of particle 2, the wave function should be one of the plus or minus states:
\...
1
vote
1answer
48 views
When exactly do identical fermions interact?
For the case of $N$ identical fermions in a three-dimensional box, the Pauli Exclusion Principle necessitates that the overall wavefunction of the system is antisymmetric. No two fermions can occupy ...
32
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5answers
6k views
Are black holes indistinguishable?
In the standard model of particles it is understood that besides characteristics like momentum, spin, etc., two electrons are indistinguishable.
Are two black holes, in the same sense, ...
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0answers
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Do the exchange operator and Hamiltonian commute for non-identical particles?
Wherever I have read about exchange operator(P), it is stated that for two identical bosons it introduces a plus sign after exchange and minus sign for fermions. P and Hamiltonian(H) commute for two ...
5
votes
2answers
274 views
Why aren't Maxwell-Boltzmann statistics used in general cases?
From Probability Theory Vol. 1 Feller Section 2 Chapter 5:
Maxwell-Boltzaman distribution: consider $r$ indistinguishable balls and $n$ cells. Assuming that all $n^r$ possible placements are ...
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3answers
185 views
Newbie question: Atom identity. How can you talk about two electrons if electrons are identical? [closed]
How can you talk about two electrons if they are identical (indistinguible)? Does it make sense to let an electron to have an identity by itself?
If they are on diferent places the place they are is ...
5
votes
3answers
215 views
Is there any “singlet state” for 3 or more spin 1/2 particles?
Every system with $N$ or more electrons lies in a Hilbert space $H=H_{\text{space}} \otimes H_{\text{spin}}$, with $H_{\text{space}}=H_{\text{space}}^{1}\otimes\cdots\otimes H_{\text{space}}^{N}$ and $...
2
votes
3answers
210 views
Decay of neutral kaon into two pions and conservation of angular momentum
I am asked the following question: A kaon $K^0$ decays into two pions $\pi^0$, being this two pions particles with spin zero. Using the conservation of angular momentum and the fact that the two pions ...
0
votes
0answers
31 views
Hilbert space of an ensemble of identically prepared systems
In order to verify experimentally the quantum mechanical predictions when we measure observable $\hat O$ on a given system A, it is usual to prepare an ensemble of identically prepared systems ($N$ ...
2
votes
1answer
58 views
Moller scattering and identical particles
Moller scattering is often described with a t-channel and u-channel.
The difference lies in the assignment whether $p_1$ changes to $p_3$ or $p_4$. Why is such an assignment valid?
Aren't the two ...
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vote
2answers
309 views
Typical application of Pauli exclusion principle in atoms
Typically when we talk about the electron orbitals around atoms we talk about them getting "filled up" starting with s1, s2, and so on (with spin taken into account as well). This relies on the Pauli ...
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0answers
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Does well-defined energy states provide a complete set of eigenstates for systems of identical particles? [duplicate]
In the usual case, we know that well-defined energy states provide a complete set of basis. Correct me if I'm wrong, but the reason is because the Hamiltonian is hermitian, therefore there exists a ...
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1answer
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Complete set of simultaneous eigenstates for identical particles
When I am learning about constructing wavefunctions for identical particles, I am taught to write down the wavefunctions of well defined energy then symmetrise them according to exchange symmetry.
...
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1answer
39 views
Condition for Slater Determinant to not vanish
We know that if the states that we put in the Slater's determinant is linearly dependent, then it vanishes.
However, is the reverse true in the sense that, if the states are linearly independent, ...
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0answers
47 views
$N$ fermions confined to a spherical shell
Consider the case where there's several identical non-interacting spin-1/2 particles with mass $m$ are confined on the surface of a sphere with radius $R$ so that the individual particles have only ...
0
votes
1answer
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Exclusion Principle for Two $e^-$ in Harmonic Oscillator Ground State
Suppose we have two $e^-$ in a one Dimensional Harmonic Oscillator with total spin $1$. I am looking for the ground state (and I've read this question Ground State Wavefunction of Two Particles in a ...
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0answers
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energy per particle in the ground state for non-interacting identical particles moving in external linear harmonic oscillator potential
Consider N non-interacting identical particles moving in an external linear harmonic oscillator potential. I want to calculate the energy per particle in ground state and show that
It is constant if ...
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1answer
103 views
Symmetrising both bosons and fermions
If I have a system of say 2 identical bosons, and 2 identical fermions, what can I say about the combined wavefunction, in terms of exchange symmetries?
Intuitively, I would expect swapping any two ...
2
votes
2answers
229 views
Are identical particles always entangled even when not interacting?
Aren't the states of two identical particles always entangled even if they are not interacting? The states of two identical particles are either symmetric or antisymmetric i.e., cannot be written as ...
0
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1answer
406 views
Ground state of three non-interacting fermions at an infinite well
In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional ...
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0answers
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Symmetrization Postulate
I just read both question here and here about the symmetrization postulate, but I have still some trouble to understand why the symmetrization postulate is needed.
If I understand well the "strongest"...
2
votes
1answer
187 views
Symmetry of Spin Function
I have a question concerning the symmetry of the spin function in multiple identical particle systems. In the solutions of one of the quizzes, my professor said that the $s=3/2$ spin function is ...
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0answers
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what does antisymmetrizing mean when it comes to electrons?
Consider two electron at $|x\rangle$ and $|y\rangle$ respectively. Is it possible to anti-symmetrize the total state of the the system just with the above information? If I make
$$|\psi\rangle = [|x\...
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3answers
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Why is Pauli exclusion principle necessary?
Why is it not possible to put two fermions in the same quantum state? I read in some book that this disturbs the quantum statistics. Also what makes bosons to have same quantum states?
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1answer
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What experiments have been done on Identical Particles?
Are elementary particles really identical, or do they have hidden state? I have learned / always assumed that any two electrons are identical and interchangeable; the same for any other elementary ...
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0answers
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Are nucleons, atoms and molecules identical particles?
Why are nucleons, atoms and molecules considered identical particles (bosons or fermions) even if they can be distinguished by the state of their most elementary components?
Also, what size does a ...
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0answers
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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 ...
0
votes
1answer
278 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
119 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 $...
8
votes
4answers
522 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.
...
2
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1answer
100 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 ...
12
votes
4answers
698 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 ...
