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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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Why are more massive white dwarfs smaller?

I understand that a neutron star 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 2 queries, one ...
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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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Levels of the $3d^2$ configuration [duplicate]

I am going through an exam question and it says the levels of a $3d^2$ configuration are $^1S_0$, $^3P_{0,1,2}$, $^1D_2, $ $^3F_{2,3,4}$ $\text{ and }^1G_4$. Obviously the $G$ state must be a ...
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The Pauli exclusion principle and the Pfaffian

We are talking about spinless fermion many-body wavefunctions. The determinant is a very nice structure for the Pauli exclusion principle, this is because when two single-particle states are the same,...
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How do I derive Pauli's exclusion principle with path integrals?

I am trying to prove Pauli's exclusion principle using path integrals. My starting point is the configuration space $\mathcal{C}$ for two indistinguishable particles in 3D: $$ \mathcal{C} = \{ \{x_1,...
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Would a neutron star-like celestial body made of bosons collapse because of missing Pauli repulsion?

Imagine the neutron star-like celestial body would be built up of bosons (assume that neutrons would be bosons). In that case there would be no Pauli repulsion (the exchange force of the exchange ...
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Identical Spin Fermions in the same orbital state: Finding total spin

Say we have two identical spin 3/2 particles in the same orbital state. What are the possible total spin? I know that there is a simple formula for adding angular momenta, but this breaks down when ...
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Intuition behind Pauli’s Principle

While reading about electronic structure of multi-electron atoms, Pauli’s Principle comes out to be a very important feature. But it feels very vague as little explanation is given about it. I mean ...
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How to derive the formula for the radius of a Fermi sphere?

I'm trying to figure out how the radius of a Fermi sphere $$p_F = \hbar (3 \pi^2 \frac{N}{V})^{1/3}$$ is derived from the formula $$dN_{spatial}=\frac{V \ d^3p}{\hbar^3}.$$ The solution states that I ...
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How does the Pauli exclusion work on fermions but not on bosons?

How does fractional spin effect the symmetry of combined wavefunctions? Why is Planck constant the universal anchor for determining if a particle is a Boson or a Fermion?
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Why do bosonic atoms behave like they do?

Why do bosonic particles behave the way they do? Why doesn't the Pauli exclusion principle affect the electrons, protons, and neutrons of the atoms at temperatures close to absolute zero? How does ...
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A possibility of the theoretical derivation of Pauli's Exclusion Principle [duplicate]

Pauli's exclusion principle tells us (in an informal language) that each and every electron in an atom is unique. When I searched for a derivation , I got nil everywhere (even the wiki site says only ...
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How can the derivation of the energy of an electron in a Fermi gas using the Heisenberg uncertainty principle be made rigorous?

When modeling a large number of non-interacting identical fermions in a potential well of volume $V$ as a harmonic oscillator and assuming the Pauli exclusion principle, it is easily seen that the ...
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Can we show that the ground state of the He atom is a spin singlet rather than triplet?

The ground state of Helium atom is a state in which the space part of the wavefunction is symmetric and the spin part is antisymmetric under the exchange of the electrons. Therefore, the ground state ...
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When exactly do identical fermions interact?

For the case of $N$ identical fermions in a three-dimensional box, the Pauli Exclusion Principle necessitates that the overall wavefunction of the system is antisymmetric. No two fermions can occupy ...
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In a quantum state, Maximum how many protons & neutrons can exist?

This is in reference to the statement I have read in a book i.e., " each quantum state can contain at the most two protons (with opposite spin) & two neutrons (again with opposite spin)". So what ...
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Pauli exclusion principle history vs. Schrödinger equation history

Why Pauli's principle of exclusion is dated before Schrödinger's equation, when Pauli didn't know about quantum numbers before Schrödinger?
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Pauli Exclusion Principle

In a box which has length $L$, there are 3 distinguishable particles which have same mass $m$ and 1/2 spin. When one is in search for lowest energy level and degeneracies, I personally think one must ...
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Do distinguishable fermions obey the Pauli exclusion principle?

We know that fermions are identical particles and obey Pauli exclusion principle. But what is meant by distinguishable fermions? Does that mean, like proton and electron both are fermions but they are ...
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Wave function of two identical quarks

I'm asked to discuss what the ground state wave functions of $qq'Q$ would look like (a combination of two quarks and some spin 0 particle $Q$ which transforms like a singlet under flavor $SU(3)_F$ and ...
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Is it possible to use force to reduce the empty space in an atom?

Atoms are mostly empty space (at least from what I've heard) so is it technically possible to shrink the space between the electrons and the nucleus of an atom?
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Pauli principle for “Phonons”

I'm reading in Feynman's "Statistical Mechanics" Chap. 6.4 about a system of $M$ interacting particles, they may be bosons or fermions. Let the hamiltonian be $$ H=\sum_i^{3M}p_i^2+\sum_{ij}^{3M}U_{...
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What is the difference between parallel and antiparallel spins for a pair of nucleons?

What is the difference between parallel and antiparallel spins for a pair of nucleons? My understanding is that nucleons have a strong tendency to pair - proton with proton, neutron with neutron, ...
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Pauli exclusion responsible for “solidity”? [duplicate]

I have heard Frank Close say that the reason you can't put your hand through a solid object is the Pauli exclusion principle. However Richard Feynman in his "Fun to Imagine" series attributes it to ...
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How does Pauli exclusion principle cause the coupling term in Weizsäcker formula?

Consider the pairing term in Weizsäcker formula. Here it is claimed that: Due to the Pauli exclusion principle the nucleus would have a lower energy if the number of protons with spin up were ...
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Term symbols and Pauli principle

Given a Silicium atom with $1s^22s^22p^63s^23p^2$ I have to write down all possible term symbols. The solution says a possibility - apart from $^1S$, $^1D$ and $^3P$ - would be $^1P$, which - due to ...
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Where does a normal force come from?

Being more specific, let's say i place an object on top of a table, this will result on the table applying a normal force on the object. My question is: Why does this force exists? Is it because of ...
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Typical application of Pauli exclusion principle in atoms

Typically when we talk about the electron orbitals around atoms we talk about them getting "filled up" starting with s1, s2, and so on (with spin taken into account as well). This relies on the Pauli ...
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Energy released by bonding between inner electron shells of atoms?

In this paper of Friedwardt Winterberg I wound section Metastable Super-Explosives formed under high pressure for thermonuclear ignition. Does it make sense? How you understand it? I'm not sure ...
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What is the formal definition of a system?

According to quantum mechanics, bosons can occupy the same quantum state in the same system but fermions cannot because the wave function for the interchange of two identical fermions would be ...
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Question about the orbits of electrons [duplicate]

A friend recently asked me the question, "If electrons have a negative charge and the nuclei of atoms have a positive charge, why don't electrons simply collapse into the nucleus and sit on it?". I ...
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Ground state of three non-interacting fermions at an infinite well

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 ...
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Has the Pauli exclusion principle been observed with neutrinos?

Has the Pauli exclusion principle been observed with neutrinos?
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Basic question on spin wavefunction

In my textbook, I am told that the $\Delta$ is a spin-3/2 particle made up of three spin-1/2 quarks. For a state with definite spin $m=-1/2$, I'm given that the spin wavefunction $$\dfrac{1}{\sqrt{3}}(...
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Can the $s=1, m_s=0$ member of the spin triplet state lead to ferromagnetic alignment?

Ferromagnetism corresponds to the parallel alignment of spins, and it is said that for ferromagnetic alignment one requires the spin part of the wavefunction must be in one of the three symmetric ...
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Symmetrization Postulate

I just read both question here and here about the symmetrization postulate, but I have still some trouble to understand why the symmetrization postulate is needed. If I understand well the "strongest"...