Questions tagged [pauli-exclusion-principle]

The Pauli exclusion principle states that two identical fermions, (so with half-integer spin) cannot occupy the same quantum state simultaneously, and thus share all of their quantum numbers. Also use for structure and classification schemes involving antisymmetry.

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What would happen if the Pauli exclusion principle did not exist? [closed]

There can be never two fermions in exactly the same state, which is known as Pauli’s exclusion principle, but infinitely many bosons. I read in the book saying that if Pauli's exclusion principle does ...
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Does degenerate matter have anything to do with the degeneracy of eigenvalues and eigenstates?

I came across degenerate matter (not the first time) after learning about degeneracy in eigenstates and eigenvalues. Are the two connected? Or is this just another use for the term?
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Pauli Exclusion principle: Query

The definition that I have concluded is that: No two fermions can exist in the state, or quantum state, unless they have opposite spins. Am I right in saying this? They can have the same azimuthal ...
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Can why electrons exist in shells be explained by the Pauli exclusion principle?

Do you know the Pauli exclusion principle?-'No two particles could be in the same quantum state at once'. Well can you use that principle to explain why electrons stay in shells and electrons in ...
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Can indistinguishable particle wavefunctions be written as a product of total observable eigenstates?

Consider the wavefunction of say two electrons in an external potential, associated with two possible states $\phi_a$ and $\phi_b$. Furthermore, each electron can have two spin states $\chi_1$ and $\...
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Virtual fermions vs exclusion principle

How QED eliminates the cases when in loop corrections two fermions get created with the same momenta and spin state? Is it done by the ladder operators? Edit: the two fermions are in two distinct ...
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Experimental evidence of Pauli principle for non-bound fermions

I mean electrons in atoms/molecules/solid bodies not count here. I heared of an experiment measuring the degeneracy pressure of a fermion gas.
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What happens if I replace an electron in a $\rm Li$ atom by a muon?

According to my knowledge the exclusion principle won't affect it, so it will jump to the muonic 1s orbit (strongly deformed by the electrons' repulsion). The electrons fill the electron 1s orbits (...
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Why is the wavefunction of a mixed-flavor baryon (e.g. the proton) antisimmetric under exchange of quarks of different flavors?

A similar question has been put before in this forum, but not with full clarity. So I would like to revisit the question and express it differently, hoping for a crystal clear answer. The question is: ...
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Could the Fermi statistic be a force?

I'm aware that, according to the Pauli principle, identical fermions obey the Fermi-Dirac statistics, so they don't occupy the same state because they just can't, it's simply how they behave. I'm ...
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Can multiple Helium-4 nuclei occupy the same place because the nuclei are bosonic?

A quarter of all matter in the observable universe is Helium-4 while all Helium-4 atoms have a nucleus with a zero spin integer which is characterized by Bose–Einstein statistics. Does this mean that ...
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Exchange Symmetry of Spatial Wave Functions in case of two Electrons and the Pauli Principle

I have some problems understanding the symmetry of spatial wave functions. In my experimental physics course they tought us that in atoms the total wave function $\Psi_{tot}(\vec{r}_1,\vec{r}_2)=\Psi(\...
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Why would one think that a solution of the time-independent Schrödinger equation is in the span of configuration state functions?

I am trying to understand why the hypothesis of configuration interaction methods is valid, i.e. I want to understand why one would think that an $N$-body wave function would be in the span of ...
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Pauli principle and Schrödinger/Pauli equations

In quantum mechanics state of the system is determined by wave function, which evolves according to the Schroedinger equation, or by Pauli/Dirac equation which are derived from Schroedinger equation ...
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Wave equation for two Fermions

I came across this basic exercise but I don't fully get the gist of it. Consider two neutral particles in a 1D Box with the interval $0\leq x \leq L$. The interaction between the two particles is ...
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Pauli exclusion principle and quantum state

Wikipedia says that two identical fermions cannot occupy the same quantum state. My question is what this quantum state means? In classical mechanics, this means that the two particles cannot have the ...
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Spin-Spin Hamiltonian in coupled harmonic oscillator

I was reading about identical particles and i came across this example: Consider two electrons with spin 1/2. The Hamiltonian for this system is: $$Η=\frac{p_1^2}{2m}+\frac{p_2^2}{2m}+\frac{1}{2}m\...
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Is there a difference between boson and bosonic?

I read about Bose-Einstein condensate consist of bosonic atoms at incredible low temperature do not obey Pauli exclusion, I am wondering what happens if it is possible to create fermionic photon for ...
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Symmetry of fermion wavefunction

I'm studying identical particles and I'm thinking about something related to fermions. I have always heard that more than two electrons can't occupy the same energy level, because their spins are ...
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Anti-symmetric property of Fermionic wave function

I am reading Quantum Statistics from 'Fundamentals of Statistical and Thermal Physics' by Frederick Reif. I have questions in two places. I understand the following paragraph: Particles with half-...
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Compatibility of spectroscopic term values with Pauli Exclusion Principle

The ground electronic configuration of Carbon is $1s^2$$2s^2$$2p^2$ $l_1=1$ and $l_2=1$ $\implies$ $L=2,1,0$ $s_1 = \frac{1}{2}$ and $s_2=\frac{1}{2}$ $\implies S=1,0$ So the terms are $^{3}D,^{1}D,^...
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How Hund's rule 1 and rule 2 prevent double occupancy?

According to Hund's rule of filling up the orbitals, the ground state electronic configuration of Nitrogen is $1s^22s^22p_x^12p_y^12p_z^1$. The electrons first singly occupy the orbitals $2p_x, 2p_y$ ...
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How does the Pauli Exclusion principle explain the incompressibility of metals?

The Pauli Exclusion principles states that no two identical fermions can have the same quantum state. In my lecture notes, it is mentioned that this principle helps us explain the fact that metals are ...
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Relation between isospin invariance and charge independence

I don't know if this question is better suited for this forum or math.stackexchange.com. I come from a mathematical background and I'm struggling to understand a passage in Lipkin's book "Lie groups ...
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What is the range of Pauli's exclusion principle?

In many introductions to the pauli's exclusion principle, it only said that two identical fermions cannot be in the same quantum state, but it seems that there is no explanation of the range of those ...
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Is the position of an electron part of his quantum state? Pauli exclusion principle

I have a problem regarding the Pauli exclusion principle which as far as I understand states that two or more identical fermions cannot occupy the same quantum state. So is the position ($r_1$) of ...
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Is the Pauli Exclusion Principle the Cause of Normal Force? [duplicate]

I'm currently studying about Dynamics in my physics class. I was looking up where the normal force comes from, and I thought that the normal force comes from Newton's third law. However, going through ...
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How does Pauli's Exclusion Principle relate to a quantum superposition of states?

Pauli's Exclusion principle states 2 fermions can not occupy the same quantum state. However, a particle can occupy a superposition of quantum states. Does this mean you can have an infinite amount of ...
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What is the intuitive physical difference between fermions and hard-core bosons?

(This is a soft question.) If we work on a discrete lattice for simplicity, then ordinary bosons are characterized by creation and annihilation operators that satisfy the canonical commutation ...
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When two identical fermions exchange, the wavefunction changes sign. Then why the statement is no new state is created?

When two identical fermions exchange, the wavefunction changes sign. Then why the statement is no new state is created now that the wavefunction is changed?
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Some questions about Dirac's sea? [closed]

Did Paul Dirac develop some way to include bosons in his formulation of the sea of particles? I have read that both electrons and anti-electrons would follow the same Dirac equation. But could there ...
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Isobaric spin $T = 0$ and Pauli-exclusion principle

I was reading a Book of Nuclear Physics (Concepts of Nuclear Physics by Bernard L. Cohen), in which he discusses the concept of Isobaric spin T and defines it by saying We see that only wave ...
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Can two fermions occupy the same energy level on a harmonic potential? [closed]

Suppose that we have a harmonic potential $\hat{V}(\hat{X})=\frac{1}{2}k\hat{X}^2$ which we will, for simplicity, consider to be one dimensional. Now let's place two fermions within this potential, ...
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If the wave function of two identical fermions is antisymmetric, how can they be identical? [duplicate]

If the wave function of a system of two identical fermions is antisymmetric, how can they be identical? I replace two 'identical' particles and get a different system. This must mean they are not ...
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How does the repulsion due to equal spin fermions show up mathematically?

I expect that in many-body problems of electrons, spin should cause same-spin-electrons to repel more strongly than opposite spin electrons because the Pauli exclusion principle is the observation ...
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Why do bosons have 0 energy in the ground state?

When looking at an ideal boson gas, it was described that at T = 0K, all the of the particles in the gas will be at the ground state, which I understand. What I don't see is why ground state is at E =...
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Are there exactly three physically relevant operators that commute with $H$ for helium?

I am thinking about something I learnt as an undergraduate. In the section on identical particles (page 212) of Griffiths book on quantum mechanics he speaks of helium and says that: The excited ...
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The antisymmetrisation of two identical single particle wave functions is identically zero, why is this important?

Let $f_1,f_2$ be two $\mathbb{R}^3 \to \mathbb{C}$-functions and $$\mathrm{asym}(f_1,f_2)(x_1,x_2) = f_1(x_1)f_2(x_2) - f_1(x_2)f_2(x_1).$$ If $f_1=f_2$ then $\mathrm{asym}(f_1,f_2)$ is identically ...
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Why 2 electrons can't be in the same quantum state when they are distant apart? [duplicate]

I understand that when 2 electrons are confined into a very small volume of space slightly bigger than their debroglie wavelength, one of the pair must jiggle with increase momentum due to pauli ...
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In electron degeneracy pressure, do electron gains mass?

I think there is no room for fidgeting but then they are still subjected to uncertainty principle, my question is when the electrons are sardine-packed to the extreme so that Pauli exclusion principle ...
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Why would sterile neutrinos not endlessly attract each other?

This question is probably far above my current understanding of physics but how do you explain why sterile neutrinos wouldn't keep falling into each other since gravity is the only force working on ...
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Is it possible to overcome pauli exclusion principle by smashing together 2 fermions really really hard?

The neutron star avoids further collapses under it's own weight due to degeneracy pressure, I was wondering beside gravity is it possible to overwhelm the pauli exclusion principle by other means such ...
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Pauli's exclusion principle in elementary particles

Elementary particles such as Quarks obey Pauli's exclusion principle since they exist in three colors (RBG). Where as electrons which is also elementary that does not have any color quantum numbers ...
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Spin-statistics theorem [closed]

I am an undergrad physics student I was curious about the validity of the Pauli exclusion principle and found that spin statistics theorem gives the prrof of this principle . What background do I need ...
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A question about quarks and quantum chromodynamics

Penrose writes the following on pg 648 of his book "Road to Reality" How can we treat quarks as real particles, if they have the wrong spin-statistics relation? The way that this problem is dealt ...
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Do anyons obey the exclusion principle?

In general, if we have two indistinguishable particles in states $\psi_1$ and $\psi_2$, then starting in the combined state $|\psi_1\psi_2\rangle$ and then exchanging them will produce the state $e^{i\...
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Exchange statistics from topology of configuration space

I'm trying to understand Leinaas and Myrheim's famous 1976 argument for exchange symmetry of the wavefunction. If we consider the configuration space $\mathcal{M}_2$ for two identical particles ...
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Bound on fermions in a finite volume?

The Pauli Exclusion Principle says that two or more identical fermions cannot occupy the same quantum state within a quantum system simultaneously. However, I'm wondering if we could potentially pack ...
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How does the Earth remain in its shape?

I know only stars do nuclear fusion to keeps its shape from gravity. Then what about the Earth? Earth doesn't do nuclear fusion. How does the Earth keep its shape even though the gravity keeps pushing ...
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Why doesn't Boltzmann Approximation obey Pauli's exclusion principle?

The difference between Fermi–Dirac function and Boltzmann approximation is that Fermi–Dirac function considers Pauli's exclusion principle but Boltzmann approximation doesn't. Why?

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