Questions tagged [identical-particles]

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

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75 views

Should entropy be always extensive?

My question came up from the discussion in class which is about whether we should treat a specific system distinguishable or indistinguishable. To figure out what will happen in these two ...
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When two identical fermions exchange, the wavefunction changes sign. Then why the statement is no new state is created?

When two identical fermions exchange, the wavefunction changes sign. Then why the statement is no new state is created now that the wavefunction is changed?
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When are particles distinguishable?

I'm just revisting some basics from statisitical mechanics for an exam. One of the exercises asks the reader to calculate the canoncial partition functions of $N$ harmonic oscillators. How should I ...
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1answer
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Are electrons and holes distinguishable particles?

In condensed matter physics: If we describe e.g. an exciton as a combination of an electron and a hole, do we need to combine them in a Slater determinant or into a simple product state? What happens ...
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Partition function of two spin 1/2 particles - Distinguishable or indistinguishable?

Suppose I have some fermions with spin 1/2 on a harmonic potential. Then the energy of each particle is given by: $$ E_i=\hbar\omega(n_{x_i}+n_{y_i}+n_{z_i}+3/2) $$ By definition the partition ...
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On the indistinguishable photons

Reading articles related to quantum optics, I have encountered the term "indistinguishable two photons" so many times. I could roughly understand what that means: two photons are very similar w.r.t. ...
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Can two fermions occupy the same energy level on a harmonic potential? [closed]

Suppose that we have a harmonic potential $\hat{V}(\hat{X})=\frac{1}{2}k\hat{X}^2$ which we will, for simplicity, consider to be one dimensional. Now let's place two fermions within this potential, ...
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Does permutation symmetry follow the Wigner's theorem?

The permutation symmetry for boson/ferminon is $$ P_{12} | 12 \rangle = \pm |21\rangle $$ I may think it as a linear unitary transformation, since $$ P_{12}^{\dagger} P_{12} =P_{12} P_{12} =1 $$ ...
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1answer
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What does Baym mean here in his Lecture on Identical Particles?

I'm reading Lectures on Quantum Mechanics by Gordon Baym (1969). In his discussion of 3-identical fermions Baym writes: "One way to make $\Psi(1,2,3)$ [the total wave-function] antisymmetric is to ...
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1answer
45 views

If the wave function of two identical fermions is antisymmetric, how can they be identical? [duplicate]

If the wave function of a system of two identical fermions is antisymmetric, how can they be identical? I replace two 'identical' particles and get a different system. This must mean they are not ...
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2answers
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How does the repulsion due to equal spin fermions show up mathematically?

I expect that in many-body problems of electrons, spin should cause same-spin-electrons to repel more strongly than opposite spin electrons because the Pauli exclusion principle is the observation ...
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The antisymmetrisation of two identical single particle wave functions is identically zero, why is this important?

Let $f_1,f_2$ be two $\mathbb{R}^3 \to \mathbb{C}$-functions and $$\mathrm{asym}(f_1,f_2)(x_1,x_2) = f_1(x_1)f_2(x_2) - f_1(x_2)f_2(x_1).$$ If $f_1=f_2$ then $\mathrm{asym}(f_1,f_2)$ is identically ...
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Identical particles in infinite potential well [closed]

I have a question about identical particles in an infinite potential well. In Zettili's quantum mechanics textbook, Section 8.5, problem 8.1(c), the Pauli exclusion principle is used to find the ...
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Triplet and singlet states: fermionic or bosonic?

Suppose we have two spin-1/2 particles with no orbital angular momentum. We choose to work with the eigenbasis of total angular momentum $S^2$ and $S_z$, which gives us the triplet and the singlet ...
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Alpha decay and Fermi-Dirac vs Bose-Einstein statistics

This article on wikipedia on alpha decay states: One curiosity is why alpha particles, helium nuclei, should be preferentially emitted as opposed to other particles like a single proton or neutron ...
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Validity of the Born approximation for identical-particle scattering

My understanding of the Born approximation is that it valid for scattering with small momentum transfer. In the context of two-particle, isotropic, elastic scattering, I would trust the Born ...
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Are atoms in a perfect crystal lattice indistinguishable?

So I was reading a wikipedia article about the third law of thermodynamics, and was intrigued by the following sentences: Suppose a system consisting of a crystal lattice with volume V of N ...
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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(...
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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 ...
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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 ...
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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: $$\...
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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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2answers
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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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687 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 ...
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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} + ... = ...
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4answers
302 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 ...
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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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1answer
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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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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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610 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 ...
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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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1answer
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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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1answer
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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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2answers
166 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 ...
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1answer
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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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1answer
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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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297 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 ...
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489 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 ...