Questions tagged [identical-particles]

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

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Distinguishable, indistinguishable paramagnetic ideal gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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62 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 ...
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78 views

Identical Particles in Non Relativistic Theory

I have a problem with the following reasoning taken from Messiah which is meant to show that there are intrinsic difficulties in identical particles which are neither bosons nor fermions. Suppose the ...
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90 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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155 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. ...
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51 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 ...
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269 views

Finding the state and wave-function for two identical spin-1 bosons trapped in one-dimensional harmonic oscillator

My question concerns the validity of my approach to a problem and wether the answer is correct. I am tasked with writing the state vector(s) and wave-function(s) for when two identical spin-1 bosons ...
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245 views

Finding the eigenstates and eigenvalues of a system of three not interacting electrons

I am trying to solve a problem on identical particles where there are three not interacting electrons. It's known that the Hamiltonian of a particle $h_{0}$ acts only on the orbital variables with non ...
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1answer
41 views

Identical particle state with spin

We construct identical particle state by symmetrizing or antisymmetrizing the tensor product of single partice states. When considering spin, a two fermions state should be $$|\psi\rangle=\frac{1}{\...
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64 views

Indistinguishability in the Ising Model

I am recently studying Statistical mechanics (In equilibrium). And get confused about that $\frac{1}{N!}$ factor when calculating the phase-space-volume. When calculating the entropy for an ideal gas ...
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48 views

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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59 views

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 identical ...
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53 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 ...
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177 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 ...
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36 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 ...
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2answers
772 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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36 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}}(...
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326 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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216 views

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 ...
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1answer
727 views

Finding states of a system of 2 identical bosons (including spin)

I'm trying to find the ground state and first excited state for 2 identical bosons in an infinite square well. I know that both states are degenerate and the spatial and spin parts of the wave ...
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163 views

Isospin and indistinguishable particles

I am trying to understand the properties of a proton-neutron system assuming that isospin is a good symmetry, so I will forget about electromagnetism, weak interactions, QCD and all those more ...
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3k views

Three particles case, finding ground energy state

Here I came up with three particles in a box problem. (Assumption: Here I do not consider the interaction between particles and spin for simplicity.) What I want to do is express the ground state's ...
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365 views

Restriction to the total angular momentum of two identical particles with spin 1

I've been asked if there is any aditional restriction to obtain the possible values of the total angular momentum J by considering that the 2 particles of spin S=1 are identical. If they are not ...
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1answer
107 views

Why two spin-$1$ bosons could not be in a spin $\frac{1}{\sqrt{2}}(|1,0\rangle-|0,1\rangle)$ state?

Consider two boson of spin $1$ without angular momentum. I'm seeing an argument that "because those two particles were bosons, they must be symmetric under the exchange $m_1,m_2$. Thus they could ...
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1answer
426 views

Identical particles: why a symetric or antisymmetric wave function?

I've read in many text books that the indistinguishability of two identical particles at $x$ and $y$ implies: $$|\psi(x,y)|=|\psi(y,x)|\quad (1)$$ This sounds rather natural. Then they say there ...
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1answer
80 views

What do we mean by “particles” when talking about identical particles in QM?

A molecule of O$_2$ and a molecule of my DNA are not identical. Therefore, some sort of restriction must be placed on the word "particle", but what sort of restrictions and why them, not others? ...
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1answer
70 views

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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47 views

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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59 views

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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41 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 ...
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58 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 ...
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36 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\...
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1answer
65 views

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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105 views

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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1answer
109 views

Identical particle exchange as a Yang-Mills theory

I am trying to find a quantum field theory (a Yang-Mills theory) for the identical particles exchange interaction. For a system of $N$ identical particles one has the state $|x_1,x_2,\ldots,x_N\rangle$...
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48 views

Is distinguishability based on the empirical fact of the distribution or is the distribution derived from distinguishability?

If two particles are indistinguishable why do we call them two or is indistinguishability just code for "count the two distinct particles together - not as two - when counting what is equilikely and ...