Questions tagged [identical-particles]

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

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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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{\...
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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 ...
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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 ...
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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} + ... = ...
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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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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?
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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 ...
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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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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?
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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 ...
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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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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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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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}}(...
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4answers
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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: \...
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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 ...
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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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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 ...
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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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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 ...
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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 $...
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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 ...
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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 ($N$ ...
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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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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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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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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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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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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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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 ...
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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 ...
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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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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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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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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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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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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 ...