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 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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Interaction between electrons obeying Pauli's exclusion principle

For fermions having half spin, obeying Pauli's exclusion principle, we know that for states with different spin states, the particles (say electrons) are distributed in such a way that if the first ...
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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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Using the Slater determinant to find the associated antisymmetric wavefunction

My lecture notes read: If there is one electron in the ground state, one in the first excited state, and one in the second excited state, why can we not instantly assume then, that: $$\phi_{n_i}(x_j)...
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Why can there be more than one electron in an energy level if electrons are fermions?

By the Pauli-Exclusion Principle, no two electrons can be in the same quantum state. So, how can both be in the same energy eigenstate? Atom orbitals certainly have more than one electron per energy ...
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Why do we have 3 quantum colours?

I understand the need to invoke colour as another quantum state to explain the observation of uuu ddd and sss baryons. I just wanted to know if there was some other property which explains why we only ...
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How are atoms supported on each other in a material?

Suppose we have a ball made up of iron. There are a "lot" of atoms in the ball. My question is "how" are the atoms supported on top of each other? And, is it due to the repulsion of electrons the ...
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Pauli Exclusion and Black Holes [duplicate]

Pauli exclusion principle states that 2 identical electrons cannot be in the same state, where state includes a spacial component. I have heard that, in order to avoid being in the same state, in a ...
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How is Pauli's exclusion principle valid for electrons of two hydrogen atoms in ground state, having same spin?

Suppose we have two hydrogen atoms in the ground state with spin of both electrons pointing upwards. Then the two electrons are in the same state. This should be against the exclusion principle. Now ...
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What is the systematic way to determine the spin of lowest-lying states of baryons like $uuu$, $ssd$, $uds$ etc?

I learned that for the lowest lying states, $uuu$, $sss$, $ddd$ can only have $J=\frac{3}{2}$ $uus$, $ddu$, $ddu$, $ssu$ etc can only have $J=\frac{1}{2},\frac{3}{2}$ $uds$ can have $J=\frac{1}{2}, \...
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Aufbau principle and quantum number $n$ (Bohr) [duplicate]

When we have to check the energy of electron we look for $n+\ell$ as in filling of electrons A/t aufbau? Or is just simply higher then value of $n$ then more the energy of electron? Because when we ...
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In the ground state of helium what's the differing quantum number?

In the ground state of the helium atom, both the electrons have the same quantum numbers $(n,l,m)$ equal to $(1,0,0)$. By Pauli's exclusion principle, the fourth quantum number must be different. What ...
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Pauli Exclusion Principle and Quantum States [closed]

We know that two identical fermions cannot be in the same state together because of the Pauli exclusion principle. My questions are: Can two bosons (for example, photons) be arbitrarily close ...
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Fermion Superposition [closed]

In case of superposition of identical particles, we usually just add their amplitudes. For example, if we have several particles having the amplitudes of being in a particular quantum state $\psi_1, \...
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Why are more massive white dwarfs smaller?

I understand that a white dwarf is supported by the Pauli Exclusion Principle and that the larger the gravitational force against them, the closer the electrons must pack. But I have two queries: ...
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Pauli Exclusion Principle and Identical Fermions

Pauli exclusion principle means no two identical fermions can be in the same quantum state. Does it mean, two electrons with the same spin cannot be in the same De Broglie Wavelength? Or, more ...
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Pauli exclusion principle for non-stable states

If an electron partially occupy $1s$ orbital, can other electron occupy $1s$ partially, too?
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When is separating the total wavefunction into a space part and a spin part possible?

The total wavefunction of an electron $\psi(\vec{r},s)$ can always be written as $$\psi(\vec{r},s)=\phi(\vec{r})\zeta_{s,m_s}$$ where $\phi(\vec{r})$ is the space part and $\zeta_{s,m_s}$ is the spin ...
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What would happen if I put two identical particles close enough?

Is there a repulsive force between these two particles to prevent them from being in the same point? I mean, in order to obey Pauli exclusion principle?
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Why is $\psi_{atom}=\psi_a\psi_b$ not a suitable wavefunction for the Helium atom?

In the approximation that the two electrons of the He atom moved independently of each other, we can say that electron 1 is in state $\psi_a(1)$ where $a$ represents the orbital quantum numbers $nlm$ ...
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Which atom numbers are possible with three bound states?

According to the Pauli principle, which atomic numbers are possible given three bound states? I know what the Pauli principle says, but I don't know how to go about finding the atomic numbers. I'm ...
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Why do neutron stars with more mass have smaller volume?

I know about Heisenberg uncertainty which makes more localized neutrons have a wider range of undefined momentum, and Pauli exclusion principle which prohibit neutrons from getting too close or "...
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How does Pauli exclusion principle work with lattice QCD?

Say your space-time lattice has 30 fermions on the vertices. (Would they have to form a path?) Swapping any two fermions (on the same row??) should make the amplitude of the lattice state negative. ...
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Exchange Interaction Time Evolution

This is a hypothetical based on a result in Griffiths (which is my level of QM understanding). In it, he derives an "exchange force" - two particles states A and B, a two-particle state composed of ...
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Example of phenomenon that occurs because Bosons don't obey exclusion principle

I am writing an essay targeted at undergrad level, non-science audience and I am trying to find another real world example of what is possible due to the fact that bosons are not subject to Pauli ...
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Can we / should we use the Pauli principle to explain band structure?

Checking the wikipedia article on band structure, I got caught in major doubts... They try to give an intuitive explanation of the band structure relying heavily on Pauli Exclusion Principle: if a ...
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The Pauli Exclusion Principle for more than two particles, applied to the Coulomb Potential

Disclaimer: I've asked a very similar question before (which I can provide if desired, but it shouldn't contain anything that is not stated here), but it was downvoted and eventually deleted for ...
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About the symmetric spatial part of a two-electron wavefunction: Can it be that $r_1= r_2$ less favoured than $|r_1-r_2|\neq 0$?

The two-electron wavefunction of the ground state of helium is $$ \psi(r_1,r_2)=\phi_{1s}(r_1)\phi_{1s}(r_2)\otimes (|\uparrow_1\downarrow_2-\downarrow_2\uparrow_1\rangle)/\sqrt{2} $$ where $\phi_{1s}...
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Is $c^{\dagger}|\psi_N \rangle= \sqrt{N+1}| \psi_N \rangle $ or $c^{\dagger}|\psi_N \rangle= | \psi_{N+1} \rangle $ in case of fermions

For the $N$ fermion state, when we apply creation operator $c^{\dagger}$, should we write the factor $\sqrt{N+1}$ with the resultant state, like $c^{\dagger}|\psi_N \rangle= \sqrt{N+1}| \psi_N \rangle ...
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Term Symbols of Carbon Atom [duplicate]

For a neutral Carbon Atom, the electron (ground) configuration is $1s^2$$2s^2$$2p^2$. I am told that the term symbols $^{3}S_{1}$ and $^{3}D_{1,2,3}$ are forbidden by Pauli Exclusion Principle. May ...

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