Questions tagged [identical-particles]

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

390 questions
Filter by
Sorted by
Tagged with
466 views

Physical meaning of symmetric and antisymmetric wavefunction

On describing Bosons and Fermions, the symmetry of wavefunction is introduced first. Here, If two particles a and b, are in two states n and k respectively, we get the wavefunction individually. On ...
• 43
101 views

What exactly does it mean for two bosons to be in the same state?

If I understand QM correctly, it's a fact that two bosons can have the same wave function in principle. What I'm wondering is if the particles governed by the wave functions can also be in the same ...
1 vote
86 views

Symmetrizing of projectors with identical particles

I am dealing with systems of $N$ identical particles in quantum mechanics. The tensor product state space is : $V^{\otimes N}$. (in the question is use the term symmetrized to designate either ...
• 254
51 views

Is it possible that a macroscopic object tends to a separable state without the need for objective collapse?

For a multi-particle system, superposition is in some sense equivalent to entanglement; with the Dirac field being treated as classical under second quantization, for example, we could at least argue ...
• 2,475
76 views

Is indistinguishability required for the stability of matter?

Classically, it is well-known that a charge-neutral system of electrons and nuclei is thermodynamically unstable. In simplistic terms, nothing in classical mechanics prevents electrons from binding ...
• 973
1 vote
46 views

Net dipole moment of identical-particle system [closed]

Let $N$ identical electric charges be arranged arbitrarily in space, in such a way that each of them has a fixed position $\vec{r}_i$, a charge $q$ and a mass $m$. If I were to calculate the total ...
• 1,616
63 views

Distinguishability in Maxwell-Boltzmann statistics

Per the Wikipedia page on Maxwell-Boltzmann statistics, the mean occupation number describes the average number of particles in the i-th single-particle state for distinguishable particles. To be ...
41 views

Fermi-Dirac Distribution for Multiple Species

If I have a system containing two types of fermions, what is the probability of a state of energy $E$ being occupied? Is it just the sum of two standard Fermi probabilities for each type of fermion?
64 views

Is a fermionic boson possible?

We know that bosons need an overall symmetric wavefunction. So is it possible for a boson to have an anti-symmetric spatial wavefunction and an anti-symmetric spin wavefunction? Such that upon ...
• 35
40 views

Is the overall (distinguishble-particle) ground state for a many-body identical particle Hamiltonian also immediately the bosonic ground state?

Consider the following many-body Hamiltonian of $N$ particles in an external trapping potential with inter-particle interactions: \begin{align} \hat{H}= \sum_{i=1}^{N} \left[-\frac{\hbar^2}{2m} \...
• 121
129 views

Calculation of canonical partition function for fermion system with degenerate energy levels

I'm having trouble in visualising the generalized version of the question asked here. We have a system with levels whose energies are $0, \epsilon, 2 \epsilon, ..., n\epsilon$, and the number of ...
47 views

If the state is VH+HV how one can prove experimentally that two photons are identical?

From a SPDC source we get two photons in a $|VH\rangle+|HV\rangle$ state. How is to be proven experimentally that they are identical while one would be in $|H\rangle$ and the other in $|V\rangle$ ...
• 651
774 views

Since anyons cannot exist in our 3+1D world, what does it mean to have discovered them? Why should we study them?

There have been previous questions on this, for example see this and this question, but my question is different. I get that in 2+1D, mathematically speaking, exchanging two identical particles twice ...
• 2,326
39 views

Normalization of one particle state wave function in fock space - commutator

In deriving the 1/$\sqrt{N!}$ normalization factor the first step is looking at the one particle state (see image below). I am confused about how we got from the first line to the second? Maybe I am ...
64 views

Operator that gives a permutational symmetry factor

Suppose that we have a system with $N$ bosonic modes, meaning that there is a vacuum state $|0\rangle$ and a set of $N$ pairs of creation-annihilation operators $a_i$ and $a^{\dagger}_i$. When ...
• 31
30 views

• 51
1 vote
60 views

223 views

Do solutions of the Schrödinger equation for multiple particles automatically obey spin-statistics?

Consider the Hamilitonian for a general two-electron system subject to an external potential $V_\mathrm{ext}$ and an interaction potential $V_\mathrm{ee}$. In this case H\psi(x, y) = -\frac{1}{2} \...
1 vote
157 views