# What is Indistinguishability: Definition and 15 Discussions

In computational complexity and cryptography, two families of distributions are computationally indistinguishable if no efficient algorithm can tell the difference between them except with small probability.

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1. ### I Electron Indistinguishability and Repulsion

If we had a system of ##N## non – interacting electrons than a wavefunction of such a system is a product of one-electron wavefunctions otherwise known as a Hartree product: $$\Psi(x_1,x_2,...,x_N) = \prod_{n=1}^N \psi(x_n)$$ This means that in such a hypothetical system , it is possible to...
2. ### I Deriving the Commutator of Exchange Operator and Hamiltonian

In the boxed equation, how would you get the right hand side from the left hand side? We know that ##H(1,2) = H(2,1)##, but we first have to apply ##H(1,2)## to ##\psi(1,2)##, and then we would apply ##\hat{P}_{12}##; the result would not be ##H(2,1) \psi(2,1)##. ##\hat{P}_{12}## is the exchange...
3. ### I How does the N signify the indistinguishability in the Gibbs Paradox?

Gibbs introduced the N! to then make S extensive. He then attributed the N! to the particles being indistinguishable. How does the N! signify the indistinguishability?
4. ### [QM] Two-Particle Systems: overlapping/non-overlapping wavefunctions

Homework Statement Hi, I was reading Griffiths and stumble upon some questions. This is from 5.1.2 Exchange Forces. The section is trying to work out the square of the separation distance between two particles, \langle (x_1 - x_2)^2 \rangle = \langle x_1^2 \rangle + \langle x_2^2 \rangle -...
5. ### Energy levels of a system with just two electrons?

Homework Statement If a system comprised only of two electrons was physically possible (such as positronium but with two electrons), what would its energy levels be and how would they relate to the energy levels of Helium? Homework Equations ##E_{Helium} = E_{n1}+E_{n2}=-\frac{\mu Z^2...
6. ### Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...
7. ### "Wavepacket of electrons" or "wavepacket of electron"?

For simplicity let's assume Gaussian shape. I just want to verify my understanding about wavepacket. As the thread title says, when we have a wavepacket, is it understood as the superposition of many plane waves corresponding to many free electrons, or as the wavefunction of only one electron...
8. ### Single photon, timing jitter, reduced indistinguishability?

I saw in a recent review paper- Engineered quantum dot single-photon sources (Rep. Prog. Phys. 75 (2012))- a discussion about how a "timing jitter" problem lead to reduced indistinguishability of single photons, which I find very hard to understand. According to the paper, for quantum-dot-based...
9. ### Many Worlds, Indistinguishability, Pascal's Triangle and the Gaussian

Suppose we have a quantity which can take discrete equally spaced values. Iteratively, we can increase or decrease this quantity by one quantum, splitting into two new worlds each time. After multiple iterations we have some indistinguishable worlds, as described by Pascal's triangle. As the...

Hey, Does anyone know a link to a paper talking about the experimental verification of indistinguishability of some free particles? For example showing it for free neutrons or something. Thanks!
11. ### Experimental confirmation of indistinguishability of identical particles?

Does the experiment confirming Bose Einstein condensation prove that identical particles are indistinguishable? How does that reconcile conceptually with Maxwell distribution to which Bose Einstein distribution converts? Is this a result of the strength of interaction among the identical...
12. ### Indistinguishability and entanglement

I have read many papers about polarization entangled photons, but in all of them, the photons need to be indistinguishable in time. But, what about the other degrees of freedom? They need to have the same frequency, energy, angular momentum? So, do they need to be indistinguishable in all degree...
13. ### Ignoring Indistinguishability

I have been asked to find whether or not indistinguishability may or may not be ignored from a given sample of atoms at a given temperature. The calculation I have done fine, but my question is given that the criterion for neglecting indistinguishability has to satisfy de broglie...
14. ### Observational indistinguishability is not equality?

Hurkyl did not explained himself on the thread, plus the question is off-topic to that thread, hence this one. So, suppose we have two models of the same thing, and all their predictions coincide. Why does it not make them equivalent? More specifically, if these are mathematical models...
15. ### Indistinguishability Of Particles

Hi, I am a student at Nottingham University England. I am currently studying for a degree in Physics, doing a second year module in Quantum Mechanics. I was just wondering if anyone could explain the indistinguishability of particles.