Questions tagged [identical-particles]
Questions related to the discernibility of many-body systems, its philosophical implications and its mathematical description.
166
questions
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3answers
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Appropriate space in second quantization
The appropriate space for the study of a system of identical bosons, for instance, is something like
\begin{equation}
\tag{1}
\mathbb{C}\oplus\mathcal{H}\oplus(\mathcal{H}\otimes\mathcal{H})_S\oplus(...
1
vote
2answers
23 views
Orbital wavefunction for a system of two electrons
I am new to this forum! I write here hoping someone can help me.
I have found a statement in my quantum mechanics book that I really don't understand.
We have a system of two electrons. If both are ...
1
vote
0answers
49 views
Are parahydrogen and orthohydrogen identical particles?
I have no formal physics background, just aerospace engineering, and I'm working on a DSMC project simulating relaxation of hydrogen in non-equilibrium, rarefied, 1D flow via translational and ...
0
votes
0answers
59 views
Grand Canonical derivation of Bose-Einstein and Maxwell-Boltzmann statistics
So, our professor introduced the Bose-Einstein statistics by deriving the Grand Canonical Partition function of a boson system associated to a single energy state $\epsilon_r$. So the formula is: $$\...
0
votes
0answers
31 views
Distance of two indistinguishable particles
Consider:
The wavefunction of a two-particle system (both Fermions and Bosons possible): $$ \psi_\pm(x_1,x_2) = \sqrt{\frac{1}{2}}[\psi_n(x_1)\psi_m(x_2) \mp \psi_m(x_1)\psi_n(x_2)] $$
And a ...
3
votes
0answers
51 views
Quantum representation of a system of identical particles
I'm studying mathematics and I began a course in quantum statistics, in which I got to the discussion related to indistinguishibility of particles. My professor's notes are not very clear and ...
1
vote
0answers
68 views
Collision between two identical particles
I was working on the exercises of the identical particles chapter of Cohen-Tannoudji, and got stuck due to some conceptual flaws. My questions are numbered below. In the problem, there are two ...
2
votes
0answers
109 views
2-level system of indistinguishable particles
It is a typical introductory problem in classical statistical physics to calculate the entropy of a two-level-system: say we have a N particle system in which particles can have energy E or 0. ...
1
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0answers
35 views
Non-Integer Values in Indistinguishable Particle Combinations Quantum Stat Mech
I am taking a thermodynamics course and we have talked about stat mech and the number of possible combinations of $N$ indistinguishable particles given degeneracy $g$.
We stated that for the ...
1
vote
2answers
67 views
Pauli Exclusion Principle and Identical Fermions
Pauli exclusion principle means no two identical fermions can be in the same quantum state. Does it mean, two electrons with the same spin cannot be in the same De Broglie Wavelength? Or, more ...
0
votes
0answers
50 views
Griffiths Quantum Mechanics - Identical Particles (Wavefunctions)
An example in Griffith's Intro. to Quantum Mechanics is:
Suppose we have two non-interacting particles both of mass $m$ in a infinite square well. The one particle states are $$\phi_n (x) = \sqrt{\...
3
votes
2answers
72 views
Confusion regarding indistinguishability of particles and the definition of Gibbs entropy
I have been reading about the Gibbs paradox, in which the assumption that particles of a monoatomic ideal gas are distinguishable leads to a paradox in which entropy is not extensive. In Schroeder's ...
4
votes
1answer
599 views
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
113 views
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
4answers
156 views
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 ...
1
vote
2answers
66 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
votes
2answers
72 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
96 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$ ...
0
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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
17 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
votes
0answers
27 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
105 views
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}
$$
where $\phi_{1s}...
1
vote
2answers
199 views
How to write equation of state in terms of partition function?
While studying quantum gases (fermions, bosons), equation of state written were $PV = k_B T Z_{gr}$, where $Z_{gr}$ is the partition function of grand canonical ensemble. $P$ and $V$ are pressure and ...
4
votes
2answers
164 views
Does quantum gases obey ideal gas equation $ PV= nRT$?
At extremely low temperature, does an ideal gas of bosons or fermions obey the ideal gas equation, $PV= nRT$?
2
votes
0answers
39 views
Spectrum of two particles system hamiltonian
Consider the following hamiltonian describing a system of two identical spin 1/2 particles in one dimension:
$$H = H_1 +H_2 - \lambda \vec {s_1} . \vec {s_2}$$
Where $H_i$ is the Hamiltonian of an ...
0
votes
3answers
418 views
Wave function of a system of two identical fermions
In N. Zettili's 'Quantum Mechanics Concepts and Applications' [chapter 8, solved problem 8.3], we have to find wave function and ground state energy of a system having two identical fermions and in ...
1
vote
1answer
56 views
Is the spin-statistics theorem true for antifermions?
The spin-statistics theorem says that having a system of identical fermions, the total wavefunction is antisymmetric with respect to exchange of any two fermions.
My question is, does this hold for ...
0
votes
1answer
48 views
Identical Spin Fermions in the same orbital state: Finding total spin
Say we have two identical spin 3/2 particles in the same orbital state. What are the possible total spin?
I know that there is a simple formula for adding angular momenta, but this breaks down when ...
1
vote
2answers
111 views
Indistinguishable particles and symmetrization of wavefunction
For 2 indistinguishable particles, we take the wave function to be
$$\psi\pm (r_1,r_2) = A[\psi_a (r1)\psi_b (r2) \pm \psi_b (r1)\psi_a (r2) ]$$
where fermions get a - sign and bosons get a +
But, if ...
2
votes
1answer
47 views
Configuration space of identical particles - fractional statistics
In Khare's book of fractional statistics and quantum theory, when discussing why we need fractional statistics he arrives at the configuration space
for a system of two identical particles in $d$ ...
1
vote
0answers
34 views
Indistinguishable particles and statistical mechanincs
i'm studying the paragraph 5.5 (page 119) of this book:
http://sciold.ui.ac.ir/~sjalali/MSc.Students/statistical.mechanics/pathria.pdf
Now at page 121 we have:
$$ \sum\limits_{p} \delta_p{u_{k1}}(...
2
votes
4answers
310 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
52 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 ...
33
votes
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, ...
1
vote
0answers
202 views
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
394 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 ...
1
vote
3answers
195 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
291 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
256 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 ...
2
votes
1answer
80 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 ...
1
vote
2answers
490 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 ...
1
vote
1answer
136 views
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.
...
0
votes
1answer
43 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, ...
0
votes
1answer
106 views
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 ...
0
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0answers
47 views
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 ...
1
vote
1answer
109 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
274 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
votes
1answer
573 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 ...
2
votes
1answer
333 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 ...
0
votes
0answers
35 views
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\...
