The tag has no usage guidance.

learn more… | top users | synonyms

2
votes
2answers
76 views

Two particles system

Source: this video For a system with two particles (09:30), why is its wave function a product of each particle's wave function? E.g. $$\psi(x_1,x_2)=\psi_a(x_1)\psi_b(x_2)$$ For indistinguishable ...
2
votes
1answer
76 views

How to understand permutations of particles in Quantum Mechanics?

I'm studying identical particles in Quantum Mechanics and I'm having a hard time to understand the idea of permutations of particles from a mathematical standpoint. From one intuitive point of view ...
0
votes
1answer
50 views

Overcounting and what is indistinguishable about indistinguishable particles?

When getting the overcounting factor in statistical mechanics, how does one compute it? Let's say each property is unique in one aspect (a string with an unique address in pc memory for example). ...
0
votes
0answers
33 views

Identical bosons with spin interactions eigenstates

Suppose that we have two particles where each of them has s=1 and it is in a harmonic oscillator potential and there is also a spin interaction. The hamiltonian of the system is :$$H=\frac{p_1^2}{2m}+\...
2
votes
3answers
88 views

Why identical particle states are multiplied?

In case of identical particles we multiply the individual wave functions of the particles to get the system wave funtion. But why are we not adding? Or performing any other operation to get the system ...
3
votes
1answer
77 views

Peculiarity about a system of three electrons

Consider three (or any number bigger than 2) electrons without spatial degrees of freedom, thus the only degree of freedom is the spins. The Hilbert space is then formed by the tensor product of the ...
17
votes
4answers
2k views

Same photon or different photon?

Consider a typical optical focusing system: A small light source, then a collimating lens, then a focussing lens, and then a detector (e.g. CCD). Assume that source intensity is so low that only one ...
7
votes
2answers
134 views

Do bosons and fermions produce the same interference pattern in a double slit experiment?

I have read that when bosons interfere they do so by adding the probability amplitudes, then I read that when fermions interfere they do so by subtracting the probability amplitudes. The usual double ...
6
votes
1answer
46 views

Why does exchanging coordinates produce a phase of $\pm 1$ in an identical particle wavefunction?

Consider a system of two identical particles described by a wavefunction $\psi(x_1, x_2)$. There are two kinds of exchange operators one can define: Physical exchange $P$, i.e. swap the positions of ...
1
vote
0answers
59 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 ...
0
votes
1answer
36 views

Implications of Indistinguishability of Particles

Wikipedia comments here on the effects of indistinguishibility of particles. Namely, it talks about the distribution of states after allowing the system (here two two level systems) interact and ...
12
votes
4answers
2k views

Why are particles in Quantum Mechanics indistinguishable?

I'm currently reading about tensor products in Quantum Mechanics and composite systems and I've read that in Quantum Mechanics particles are indistinguishable while in Classical Mechanics that's not ...
9
votes
1answer
224 views

Identical particles and topological phases

I've been wondering about the argument that is always put forward for why the only possible identical particles in three dimensions or more are bosons or fermions. My question is related to a very ...
1
vote
0answers
42 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 ...
1
vote
2answers
110 views

Doesn't the success of statistical physics seem somewhat unreasonable?

It seems to me a rather big coincidence that statistical physics works so well. I can see how consistent macroscopic observations can occur just because the microstates that give rise to that ...
2
votes
1answer
49 views

Matrix in two boson system

If there are $N$ single-particle states labeled by $1,2,3,\cdots,N$, it is said that the general two-boson state is given by $$|\Psi\rangle=\sum_{i,j=1}^N \omega_{ij}a_i^\dagger a_j^\dagger |0\rangle$...
0
votes
0answers
54 views

Question about CSCO for identical 1/2 spin particles?

I have two, identical 1/2 spin particles which interact through the hamiltonian $$H = \frac{p_1^2}{2m} + \frac{p_2^2}{2m} + V(|\vec{r_1}-\vec{r_2}|) $$ and I have to determine the observables that ...
3
votes
1answer
88 views

“distinguishability” of 1D identical particles

Recently when I deal with 1D electron system, it occurred to my mind that since these electrons are not able to bypass each other during the scattering processes, we can actually label them as the 1st,...
1
vote
1answer
47 views

About bosonic, fermionic state in identical particles

The upper picture is my ideas which represent states by using the tensor product. but the lower picture, as you see, includes uppermost states. i don't know how to treat the uppermost states in lower ...
1
vote
0answers
42 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 ...
3
votes
2answers
86 views

How can we “exchange” particles, since they are “identical”?

Doubt 1: If two particles are identical, you can not distinguish between them. Then, I think, permutation operation is meaningless. Because you can not distinguish them, how can you tell if they are ...
1
vote
2answers
138 views

The statistical interpretation of Entropy

I recently got introduced to the Statistical Mechanics, particularly, the Statistical Interpretation of Entropy and am utterly confused regarding the following problem: Imagine a box with two ...
-1
votes
1answer
105 views

Is this a good argument against time travel? [closed]

Two fermions in two different points of space cannot be made to exist in the same point of space. It follows then that two fermions in two different times cannot be made to exist in the same time. ...
4
votes
1answer
225 views

Why must fermions be antisymmetric? [closed]

I have read that fermions cannot exist in the same state simultaneously. I understand why indistinguishable particles with an antisymmetric superposition of states can't exist in the same state ...
1
vote
1answer
58 views

Identical particles: Why only two possibilities?

Given two identical particles, Wikipedia says that the wavefunction of a combined system where the first particle is in state $|n_1\rangle$ and the other one is in $|n_2\rangle$ is $|\psi\rangle=|n_1\...
0
votes
1answer
159 views

No two identical fermions can have the same quantum state at once?

This is the Pauli Exclusion Principle, but I have a question about it... It states that no two identical fermions can have the same quantum state, but what about different fermions having the same ...
0
votes
2answers
433 views

Why are electrons alike but photons not?

Perhaps this is a misconception, but why are electrons alike and photons not? Given two photons, they may differ by having different frequencies (energies). Given two electrons, there are just two ...
2
votes
1answer
92 views

Diagonal part of the configuration space of two indistinguishable quantum particles

Why is the configuration space of two indistinguishable particles given by $\frac{M^n-\Delta}{S_n}$? My question is about the $\Delta$. (Notation: $M$ is the configuration space of 1 particle. $M^n$ ...
3
votes
1answer
381 views

About the factorial N! in the partition function

After reading these posts: Why is the partition function divided by $(h^{3N} N!)$? , What is the resolution to Gibb's paradox?, and some of these: http://arxiv.org/abs/1012.4111 , http://bayes....
9
votes
4answers
558 views

Why is the partition function divided by $(h^{3N} N!)$?

When computing partition functions for classical systems with $N$ particles with a given Hamiltonian $H$ I've seen some places writing it as $$Z = \dfrac{1}{h^{3N} N!}\int e^{-\beta H(p,q)}dpdq$$ ...
1
vote
1answer
96 views

Are all ground state protons the exact same mass and have the same number of elementary particles?

I have read that it is a misconception that a proton only has 3 quarks (2 up and one down). In reality, it seems there are many, many ("zillions" is the number I saw quoted) quarks in a proton. Do ...
0
votes
2answers
32 views

Enforcing the exchange criteria for two particles in a box in different states

Suppose you have two identical particles (for simplicity we can think of spin 0 bosons for which are represented as a scalar wave-functions, but fermions have a similar problem) in a 1D box that ...
0
votes
0answers
52 views

Summing over quantum states

For a system of $N$ identical particles we deal in quantum mechanics with wave functions $\langle \{\mathbf{r}_i \} \mid \Psi \rangle=\Psi(\mathbf{r}_1,\dots,\mathbf{r}_N)$ from which determine the ...
-1
votes
3answers
154 views

What logical/mathematical proof do we have to show that, everything which is called electron are identically the same? [duplicate]

Premise 1: Physics don't believe in sense "organs" of the human "robot" (more commonly said "common sense deceives us"). Premise 2: Physics believes in logic or mathematics. Background thrust: ...
1
vote
1answer
162 views

Meaning of the symmetrisation postulate in absence of a proper model

My question is on the use of the concept of indistinguishable particles (in quantum mechanics) in a very general context and in particular in statistical mechanics. I have made clear some of my ...
0
votes
2answers
133 views

multiverse fabric of reality

Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from ...
1
vote
1answer
96 views

How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states. Each one of them can be uniquely determined by total spin and its orientation, we can use $...
1
vote
1answer
172 views

Why two-particle wavefunctions are separable and their corresponding particles are indistiguishable at the same time?

If the wavefunction $\psi(r_1,r_2)$ doesn't represents an entangled state, it is separable: $$\psi(r_1,r_2)=\psi_a(r_1)\psi_b(r_2)$$ In this treatment, we ignore the interaction between two particles ...
5
votes
2answers
398 views

Bose Enhancement Factor

How may one explain the fact that the probability of a boson transferring to a state with an occupation number n is 'enhanced' by a factor of (1+n), compared to the classical case? (In the classical ...
0
votes
2answers
380 views

Indistinguishable particles and probability density

I am given the following (probably simple) exercise, but I think I misunderstand something: Let $\psi_{a,b}(r_1,r_2)$ be a two-particle state, calculate the probability density for distinguishable ...
0
votes
1answer
185 views

Two Particle System with Identical Particles

I'm studying for an exam in quantum mechanics and tried to calculate the ground state and the first two excited states of two identical bosons (spin 0) in an infinite one dimensional potential well. ...
2
votes
2answers
330 views

Is a superposition of (anti)symmetric states (anti)symmetric?

Let's say we have the following wavefunction of two identical particles, $A$ and $B$: $$\frac{1}{2}[(\chi(A)\psi(B)\pm\psi(A)\chi(B))+(\phi(A)\eta(B)\pm\eta(A)\phi(B))]$$ Is this properly (anti)...
4
votes
0answers
164 views

Interchange symmetry for states with identical particles

I was reading this web page about interchange symmetry for states with identical particles here: http://quantummechanics.ucsd.edu/ph130a/130_notes/node317.html The article states that the highest ...
5
votes
2answers
269 views

Representation of indistinguishability in quantum mechanics

I was wondering that if particles are indistinguishable in quantum mechanics, then why do we still express their states $\left| \uparrow \downarrow \right\rangle$, as meaning particle 1 (in the first ...
6
votes
2answers
470 views

Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
2
votes
2answers
97 views

Identical Particles, Why and How?

I know this question is going to be borderline philosophy, but please humor me. What is the significance oh identical particles? I can understand that two particles can be identical, but then it ...
5
votes
2answers
1k views

Grand canonical partition functions for Bose-Einstein statistics vs. Maxwell-Boltzmann statistics

In Bose-Einstein statistics, the grand canonical partition function is $$\mathcal{Z}=1+e^{-\beta(\epsilon-\mu)}+e^{-2\beta(\epsilon-\mu)}+e^{-3\beta(\epsilon-\mu)}+\cdots$$ In Maxwell-Boltzmann ...
0
votes
1answer
575 views

Symmetric, antisymmetric and mixed symmetry particles

Can someone explain to me the concept of symmetric, antisymmetric, and mixed symmetry when talking about the states of identical particles?
7
votes
2answers
679 views

What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
11
votes
5answers
2k views

Is the $N$ factorial in the Partition function for $N$ indistinguishable particle an approximation?

I suspect that the $N$ factorial in the partition function for N indistinguishable particles $$ Z = \frac{ Z_0^N } {N!} $$ is an approximation. Please someone correct me if I am wrong and why or why ...