What is Identical particles: Definition and 68 Discussions
In quantum mechanics, identical particles (also called indistinguishable or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules. Quasiparticles also behave in this way. Although all known indistinguishable particles only exist at the quantum scale, there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability, as explored in quantum statistics.
There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which cannot (as described by the Pauli exclusion principle). Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei.
The fact that particles can be identical has important consequences in statistical mechanics, where calculations rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.
I am reading the Schwartz's quantum field theory, p.207 and stuck at some calculation.
In the page, he states that for identical particles,
$$ | \cdots s_1 \vec{p_1}n \cdots s_2 \vec{p_2} n \rangle = \alpha | \cdots s_2 \vec{p_2}n \cdots s_1...
a) Find the energy levels of the ground state and the first excited state.
b) Find the wave functions (in the coordinate representation) of the ground state and the first excited state.
Hints: For a particle of mass m in a harmonic potential of angular frequency ω, the energy of the particle in...
Problem: A system contains two identical spinless particles. The one particle states are spanned by an orthonormal system ##|\phi_k>##. Suppose that particle states are ##|\phi_i>## and ##|\phi_j>## (##i \neq j##). (a) Find the probability of finding the particle in the state ##|\xi>## and...
Is it possible to derive special relativity from the principle of quantum mechanics according to which particles of the same type are indistinguishable?
For example, if it is not possible to distinguish particles of the same type then particles colliding in a train at constant speed should...
My thoughts are:
a) it should just be N^2
b) just N since they're identical
c) due to Pauli exclusion would it be N^2 - N since they have to be different states?
assume i have a gass made from N identical particles in a box and i want to calculate the probability for k out of N particles to be in the left side of the box.
the problem is ,that if we treat the N particles as identical , each state in which exacly k of the N particles are in the left side...
Can someone help me with this excercise?: Consider two electrons constrained to move in one dimension. They interact through the potential
$$
V(x) = \begin{cases}
0, & \text{ if } |x| > a \\
-V_{0}, & \text{ if } |x| \leq a
\end{cases}
$$
where ##x## is the relative coordinate. The total spin is...
In my lecture notes, the normalisation for such a bosonic state was given by
However, I can't quite seem to grasp how the normalisation factor came about. Could someone walk me through it? Many thanks in advance!
Homework Statement
So in my problem, there's a given of 3 non interacting fermions in a harmonic well potential. I already got the wavefunction but i have problems in obtaining the ground state energy and its 1st excited state energy for 3 fermions (assuming they are non interacting and...
Is it possible to take two identifiably different particles of the exact same type (I previously called them indistinguishable in error?) which have different quantum states (say a different distribution in position or momentum Hilbert space) and physically cause them to have identical states...
Homework Statement
The ground state energy of 5 identical spin 1/2 particles which are subject to a one dimensional simple harkonic oscillator potential of frequency ω is
(A) (15/2) ħω
(B) (13/2) ħω
(C) (1/2) ħω
(D) 5ħω
Homework Equations
Energy of a simple harmonic oscillator potential is
En...
The concept of Identical Particles in non-relativistic QM seems a little shakey to me. All elementary particles of a certain type, say electrons, are supposed to be identical except for a handful of degrees of freedom like spin direction, position, etc. (For some reason, energy and momentum...
Homework Statement
Hi, I was reading Griffiths and stumble upon some questions. This is from 5.1.2 Exchange Forces. The section is trying to work out the square of the separation distance between two particles, $$\langle (x_1 - x_2)^2 \rangle = \langle x_1^2 \rangle + \langle x_2^2 \rangle -...
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...
In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional infinite potential well of length a. He states that one possible configuration of the ground state...
Homework Statement
Show that it is impossible for an ultra-relativistic particle with ##pc>>Mc^2## to disintegrate into two identical massive particles of mass m.
Homework Equations
Conservation of four momentum
The Attempt at a Solution
The four momentum of the ultra-relativistic particle...
From Weinberg's Quantum Theory of Fields Vol. 1, Chapter 4. Under interchange of two identical species of particles we have:
\begin{equation}
\Phi_...p,\sigma,n...p',\sigma',n...= \pm \Phi_...p',\sigma',n...p,\sigma,n...
\end{equation}
Plus sign for bosons and minus for fermions. As far as I...
This is the problem I'm trying to understand:
Consider two particles with spin 1 without orbital angular momentum. If they are distinguishable, from the rule of addition of angular momentum applied to spin, we'll have states of total spin j=0,1,2. If we have, however, identical particles which...
I have an "unidimensional" box with two identical particles in. My question is , Does it matter in which total spin state is my total function? I mean , if it is a singlet or triplet , one is antisymmetrical and the other is symmetrical, but I only integrate the function in the spatial...
Homework Statement
Two identical particles, each of mass m, move in one dimension in the potential
$$V = \frac{1}{2}A(x_1^2+x_2^2)+ \frac{1}{2}B(x_1-x_2)^2$$
where A and B are positive constants and ##x_1## and ##x_2## denote the positions of the particles.
a) Show that the Schrodinger equation...
Hey there,
I am familiar with the mathematics of multi-particle systems, but have now moved on to trying to plot them. I was a little ambitious and thought I'd attempt to somehow plot energy eigenfunctions of two particles in a 2-D box. Obviously I immediately ran into the issue that there are...
On page 9 of *Quantum theory of many-particle systems* by Alexander L. Fetter and John Dirk Walecka, during the derivation of the second-quantised kinetic term, there is an equality equation below:
>\begin{align}
\sum_{k=1}^{N} \sum_{W} & \langle E_k|T|W\rangle C(E_1, ..., E_{k-1}, W...
I am relatively well versed when it comes to systems of spin, or doing the maths for them at least, but am unsure whether all of the {L2, Lz, (other required quantum numbers)} basis eigenstates for a general system of n particles of spins si, where si is the spin of the ith particle, can...
Is it possible to have identical quantum particles that are distinguishable? By identical, I only mean that all particle properties like mass, spin, charge, etc., are identical. My guess would be no because the only thing that could tell the two apart is their trajectories, but their...
Consider a system of two identical spin-1 particles. Find the spin states for this system that are symmetric or antisymmetric with respect to exchange of the two particles. (Problem 13.3, QUANTUM MECHANICS, David H. McIntyre)
I know that for bosons, the total wavefunction should be symmetric...
Hello.
It is said that if we exchange two electrons, we can't tell which is which. Identical mass, charge, etc. So if I hold two electrons, one in each hand, and someone switched them, I wouldn't be able to know. But one way to distinguish particles is their trajectory. If I have a very long 1D...
The probability of finding one single particle at energy ##\epsilon## in a system of such distinguishable particles at thermal equilibrium in the thermodynamic limit is given by the Boltzmann distribution that is: (up to a constant factor in front)
##e^{-\frac{\epsilon}{kT}}##
To find this...
I hope somebody is familiar with the discussion on the identical particles in Quantum Mechanics by L. Ballentine. In particular can someone help me explain how the author derive equation (17.44) from (17.41). In case your edition is different from mine, equation (17.44) is the one which looks...
1. Problem: Consider the composed system of two particles of spin ##s=1## where their angular momenta is ##l=0##. What values can the total spin take if they identical? What changes when they are distinguishable?
The Attempt at a Solution :
The problem I have here is incorporating the fact...
In Introduction to QFT (peskin) 4.5, he writes:
The computation for M, of course, will be quite different when identical particles are present.
However, I have finished reading the first part of the book and found no special treatment for identical particles. Can anybody tell me how to...
I am learning identical particles recently, but I have some problem interpreting what I am writing down. So if we have two distinguishable particles, absolute value of ψ(x_1, x_2) tells the prob. density of finding the first particle at x_1 and the second at x_2. But for identical particles, it...
If a particle of mass M is at rest in a lab when it decays into 3 identical particles of mass m with:
particle 1: having a velocity of 4c/5 in the -i direction vector
particle 2: having a velocity of 3c/5 in the -j direction vector
particle 3: having an unknown velocity in a direction defined...
Homework Statement
Two identical spin-1/2 particles interact with Hamiltonian H0=ω0 S1.S2 where ω0>0. A time dependent perturbation is applied, H'=ω1 (S1z-S2z) θ(t) Exp[-t/τ], where ω1>0 and ω1<<ω0. What are the probabilities that a system starting in the ground state will be excited into each...
hello guys , in this problem from zettili quantum mechanics that i attach , i think something is wrong , first the problem said two particles with spin 1/2 but didn't mention that the system is in singlet state or triplet state , so if the system be in triplet state then our spatial wave...
When combining N spin 's' states, is it always true that each multiplet has even or odd symmetry?
I know that's the case for N=2 and s=1/2 or 1. For s=1/2, the triplet is symmetric and the singlet is antisymmetric. For s=1, the pentlet is symmetric, the triplet antisymmetric, and the singlet...
In Weinberg's textbook on QFT(google book preview), he discussed the phase acquired after interchanging particle labels in the last paragraph of page 171 and the footnote of page 172. It seems he's suggesting interchanging particles of same species but different spin states will only bring a...
The undistinguishable principle of identical particles says we can not distinguish the identical particles.But I think that two electrons(for example) having the wave packets that are separated with each other are distinguishable(?).
Can we distinguish two particles that their wave packets...
Hi. Say you have a cluster of particles and you are probing the cluster with a dopant particle. You excite the dopant and observe its emission - this spectra is perturbed by the cluster particles compared to the free dopant.
What if the dopant was the same as the cluster particles. I know you...
Dear All:
I have a quite mysterious and cumbersome question concerning with the expectation values for a system of identical particles. For example, suppose I have a system of N identical bosons given by the wavefunction ψ(x1,x2,...xN), which is of course symmetrized. My concern is:
1...
Hello Everyone,
I've come across the following question and can't seem to get the right answer out:Homework Statement
Two identical particles are in an isotropic harmonic potential. Show that, if the particles do not interact and there are no spin-orbit forces the degeneracies of the three...
I'm just wondering if it's possible (if there's a paper or some such that'd be great) to derive quantum mechanics or quantum field theory WITHOUT invoking the notion of identical particles to prove things like Pauli's exclusion. Anyone know?
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...
Why are identical particles indistinguishable? (Note that I only take the usual Hilbert space formalism as a given)
I've heard the very vague argument of "two waves overlapping and you can't say which is which" but of course physicists should be able to do better than that.
So does it...
Hey I'm tring to grasp the symmetrization principle for identical particles. If the particles are indistinguishble, for example two electrons (not regarding spin), then \psi(x_1,x_2) must correspond to the same physical situation as \psi(x_2,x_1). It follows that
|\psi(x_1,x_2)|^2 =...
Homework Statement
So, I'm asking for a bit of help before I confuse myself completely.
The question statement is:
Consider a two-dimensional potentialbox
V(x,y) = 0 if 0 \leq x \leq a, 0 \leq y \leq 2a
and infinity otherwise.
a) Determine the energy eigenstates and energy...
For two particles which have identical physical charges (say under electromagnetism), are the bare charges necessarily the same? Since the physical charge is related to the bare charge by photon and particle renormalization factors, I don't see how this could be the case in general.
In some...
Hi there:
I have a somewhat strange/vague question and hoped that someone here could point me in the right direction to find a solution.
I have a system comprising of a number of identical particles (i.e., I can't differentiate between them) in 2-D space. I have numerous observations of...
Final distance between two charged, identical particles approaching each other
Homework Statement
Two identical particles, each with a mass of 4.5 mg and a charge of 30 nC, are moving directly toward each other with equal speeds of 4.0 m/s at an instant when the distance separating the two...
hello,
can we say that identical particles in atoms like electrons are entangled since their total wavefunction is antisymmetric when we swap the states?
is there any condition for this entanglement?