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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 ...
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2answers
71 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 ...
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1answer
48 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. ...
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2answers
83 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 ...
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0answers
74 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 ...
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2answers
130 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 ...
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2answers
97 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 ...
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2answers
64 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 ...
4
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2answers
337 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 ...
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1answer
99 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?
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5answers
1k 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 ...
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4answers
4k views

Are atoms unique?

Do atoms have any uniquely identifying characteristic besides their history? For example, if we had detailed information about a specific carbon atom from one of Planck's fingerprints, and could ...
0
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1answer
125 views

Total angular momentum in a full shell

I do not understand why it's supposed to be vanishing. Rather than discussing the question in its full generality I prefer to consider the following scenario, which I think sums up anything that's ...
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2answers
402 views

Electrons, spins, and degeneracy

In an atom, two electrons can have the same set of $n,\ell,m$ quantum numbers as long as they have opposite spins. My introductory physics and chemistry courses have all introduced this as two ...
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2answers
164 views

Is there is a reason for Pauli's Exclusion Principle?

As a starting quantum physicist I am very interested in reasons why does Pauli's Exclusion Principle works. I mean standard explanations are not quite satisfying. Of course we can say that is because ...
10
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2answers
522 views

How are anyons possible? (another version)

I know that this question has been submitted several times (especially see How are anyons possible?), even as a byproduct of other questions, since I did not find any completely satisfactory answers, ...
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2answers
220 views

How axiomatic is the symmetrization requirement (i.e. the Pauli principle)? (in QM)

I've so far always been told, that the symmetrization requirement is an axiom on the level of the Schrödinger equation and the statistical interpretation of the wave function (or it's absolute value). ...
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1answer
1k views

Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by ...
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1answer
164 views

Aren't all electrons the same? So what about electron that absorbs photon?

I learned that electron absorbs a photon and goes into higher energy state. But also all electrons are identical. What is a difference between the electron in low orbital energy state? and the high ...
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3answers
363 views

What are the differences between indistinguishable and identical?

What is the difference between indistinguishable particles and identical particles?
4
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1answer
452 views

Proving that the free energy is extensive

If I have two system of an Ideal gas $A$ and $B$ each of these system has a partition function: $Z_{A,B} = \left ( \frac{V_{A,B}}{\lambda_T} \right )^{N_{A,B}}$ Where: $\lambda_T = \left ( ...