# 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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
41 views

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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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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? ...
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 ...
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. ...
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 ...
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 ...
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 ...
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\...
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 ...
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 ...
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 $|x_1,x_2,\ldots,x_N\rangle$...