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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In Helium, why does more tightly bound mean the electrons are further apart?

In helium, the triplets ($S=1$) are lower in energy (more negative) than the singlets $S=0$. One reason given by my lecturer is that in a triplet the spins of the two electrons are the same, then by ...
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Pauli's principle on two-electron system

I just have been introduced to the axiom "defining" bosons and fermions, namely (for fermions): Consider a collection of $N$ identical particles moving in $\mathbb{R}^3$ and having a (half-...
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Taking into account the Pauli Exclusion Principle, how many particles can you cram into a really small space?

I'm trying to understand the basic concept of the Pauli Exclusion Principle, but my former question here did not provide an answer. So let me rephrase it. One way of describing the PEP is that you ...
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If a spin singlet cannot change, how can it interact with electromagnetism?

Let's say there's a Hydrogen atom in a spin triplet state. $$ | \downarrow\downarrow \rangle$$ Now let's say a photon with spin 1 came along abs was absorbed by the atom. We don't know if the proton ...
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How many states are possible for two (indistinguishable) electrons with $n=2$ in an atom if we forget Pauli’s exclusion principle?

I have been told I can use $^8C_2 = 28$ to obtain the answer to this question, but I am doubtful of this result since I obtain $21$ by simply writing out the possible states as ($ml_{1}$, $ms_{1}$, $...
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Just how small a point is required for the Pauli Exclusion Principle to apply when looking at LQG?

In Loop Quantum Gravity, the thought is that the smallest possible point is 10^-35 meters. But it is recognized that this is still not a singularity, which basically has no dimensions. So when it ...
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Two identical fermions in a box and the spin-statistics theorem

Consider the case of two identical non-interacting spin 1/2 particles in a box, whose length is $L$ with walls at $x=0$ and $x=L$. The Hamiltonian in this case (setting $m=1/2$, $\hbar=1$) is $$ H=H_1+...
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Do entropic forces inherit de-facto force carriers from confinement?

Do entropic forces inherit force carriers from the forces responsible for the confinement that gives rise to the entropic force? What if you have multiple different fundamental forces combining to ...
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What happens in PEP interactions at energies lower than excitation energies?

Suppose two helium atoms bump into each other with less kinetic energy than would be required to promote one of the atoms in isolation to an excited state. The following is my understanding of the ...
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Pauli exclusion principle in case of electron-positron anhillation?

Pauli exclusion principle says that no two particles can occupy a single Quantum state and that prevents electron from falling into the nucleus. But then, what about electron-positron annihilation, ...
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All forces break down into the four fundamental forces/interactions ― Is this really true?

So there is this notion that all forces can be broken down into the four fundamental forces/interactions. However, I'm starting to wonder if that is really true. The solidity of matter is explained ...
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How do expression of Fermi–Dirac distribution leads to explanation of Pauli exclusion principle

I am beginner in statistical mechanics and found a question asking to show how Fermi-Dirac distribution leads to the explanation of Pauli exclusion principle. I know how to derive Fermi-Dirac ...
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Bounds to the pauli principle

There cannot be two or more Fermions in one quantum state. A quantum state is defined by a full set of observables / operators. For example, in the case of an electron in the H atom it is $H, L^2, L_z$...
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Can the Pauli exclusion principle and quantum tunneling coexist? [closed]

It is said that quantum mechanics can pass through walls. In addition, there is a possibility that the body will be disassembled and then reassembled. By the way, doesn't Pauli exclusion principle say ...
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Degeneracy of an energy level and Pauli Principle

I am a bit confused as to how these two concepts interact together. I'd like to discuss it with a simple example, that of the electrons in an atom. I am also not considering fine structure and HFS. If ...
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Degeneracies for Fermions and Boson like Electrons

Consider the helium atom to be a fixed point nucleus (with charge 2$e$) with two spin-half fermion electrons. What is the degeneracy of the ground state? If the two-electron was a spin-half boson, ...
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Are paired electrons not bosonic?

A pair of electrons has spin 0 which makes any such system a boson rather than a fermion. The Pauli exclusion principle does not apply therefore to paired electrons and any such two electrons can ...
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Could electrons tunnel into protons in a white dwarf and turn it into neutron star?

Just like the Sun, where hydrogen ions tunnel into each other to start fusion, which would be otherwise impossible with this level of kinetic energy, could electrons inside a white dwarf tunnel into ...
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Why neutron degeneracy pressure is much stronger than electron degeneracy pressure?

I am asking about Pauli Exclusion Principle stating that no two fermions can have the same 4 quantum numbers which is why we have periodic table of elements, but straight to my question: despite Pauli ...
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Covalent bond between two hydrogen atoms with the same electron spin?

According to Pauli's principle, two electrons in an orbital cannot have the same spin. Does this mean, for example, that two hydrogen atoms, each with one electron, will not covalently bond to H2 if ...
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System boundary for two electrons that obey exclusion principle

The exclusion principle makes a good sense to me mathematically but not so much physically intuitive. Suppose we have a quantum system of two electrons. Now if they are on a metal thin film they ...
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Why can strange matter be sensible and motivated by the Pauli Exclusion principle?

I have heard of strange matter as a way "relieve" the Fermi degeneracy pressure, but I do not understand why exactly. Since quarks are coloured they already have a different quantum number ...
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Why aren't triplet states in Hydrogen molecule bound by Pauli's principle?

I am learning about the wavefunction of two electrons in a Hydrogen molecule and I came across following spin states: |↑↑⟩ and |↓↓⟩, which form two of the triplet states in the molecule. This confuses ...
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How can neutral, even-numbered atoms like strontium be trapped in a magnetic trap?

Since the beginning of this year, there has been a lot of attention paid to newly-created 'Pauli crystals', also known as 'Pauli-blocking crystals'...... Using ionized atoms, or at least odd- numbered ...
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How can the exchange interaction make electron spins parallel?

Electrons repel by Coulomb interaction. When they get too close, Pauli exclusion principle ("Exchange interaction") becomes important. If their spins are parallel, they are further "...
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Energy levels in tetrahedron

Let us consider tetrahedron with vertices, labeled as 1, 2, 3, 4. Let us have $N$ electrons which can be placed in this vertices. Let the hamiltonian of this system satisfy such condition: $$ \langle ...
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Is it impossible for anything to touch anything else because of Planck lengths?

Suppose you touch a cube. There would still be a Plank length between your hand and the cube. Does this mean that it is impossible for anything to touch anything, specifically because there is always ...
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Why is the Pauli's exclusion principle not violated in the two neutron beams interference experiments?

It is my understanding so far that in this kind of experiments like the one measuring the 4π (i.e. 720° Dirac Belt trick) rotation characteristic of 1/2 spin fermions like neutrons, two neutron beams ...
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Confused about the Pauli exclusion principle

I've been struggling to understand this: Let's say I have a gas of one million electrons. Does every single one of those electrons have a different energy (up to the degeneracy from the different ...
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Pauli exclusion principle and antimatter

Have the Pauli exclusion principle been proven to apply to antimatter experimentally?
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What really supports neutron stars?

I have read this question (to Andrew's answer, in the comments): What supports neutron stars is the repulsion provided by the strong nuclear force between closely-packed neutrons. The central ...
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How to count the number of microstates in this example and in general

Suppose we have $3$ energy levels $E_1,E_2,E_3$, that we need to fill up with $3$ electrons. Each of these Energy levels can be filled with two electrons - spin up and spin down. How does one ...
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Fermions in a micro-canonical ensemble

I've been reading statistical mechanics, and I read the following on Wikipedia, on the article on Fermi-Dirac Statistics derivation in the micro-canonical ensemble : Suppose we have a number of ...
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Linear combination of Slater Determinants

I've been reading about many particle states in quantum mechanics and came across the fact that combinations of fermions can be represented using a Slater determinant. This is quite easy to understand ...
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If there are huge gaps between atoms relatively to their size, why can we touch things? [duplicate]

Most of the volume of an object actually consists of empty space rather than molecules. So why don’t solid objects move through each other?
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Big Bang and the Pauli Exclusion Principle

Due to some of the basic principles of quantum mechanics, we have the Wolfgang Pauli exclusion principle, where two fermionic bodies cannot occupy the same quantum state simultaneously. If that is ...
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Two electrons in the ground state

I've been introduced to multiple particle systems in quantum mechanics, and in the case of the $2$-electron system, I'm facing this massive confusion. In the ground state of a $2$-electron system, you ...
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Pauli Exclusion Principle Violation, Why is Energy Quantized?

The orbitals of an atom can be thought of as being formed from the probability of finding electrons in those orbitals. If the orbital is 1s (n = 1, l = 0), then it has a certain "volume" for ...
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How do Fermi-Dirac statistics contribute to fermions in the Pauli Exclusion Principle?

So I’m doing some research on Quantum Chromodynamics and I've come to an area in which I’m having some trouble arriving at a conclusive answer. Apparently the Pauli exclusion principle states that no ...
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Interference between fermions in square well

Are identical fermions in a square well interfering with each other? My qm class taught the double slit experiment using single particle wave functions. Unfortunately, I do not have a good reference ...
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Is Pauli's exclusion principle a postulate of Quantum Mechanics?

Is Pauli's exclusion principle a direct consequence of the postulates of Quantum Mechanics or is it an independent postulate? For instance if one asks, Why are there particles that follow Pauli ...
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Normal Force in Elevator

I've recently been studying Newton's laws of motion and came across this example of apparent weight in an accelerating elevator. Taking the upwards direction as positive, when the elevator is ...
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Does the electron capture process ever occur in hydrogen?

I know that electron capture occurs more readily in heavier, often unstable atoms, but does it ever happen at all in a lighter atom? I suppose, in ordinary hydrogen, a free neutron would then be ...
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Superposition of states of different fermion number

Physically, can quantum-states which are a superposition of states of different numbers of fermions exist? i.e. states of the form $\vert \psi \rangle = a \vert N\rangle + b \vert N' \rangle$ where $N ...
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When is it necessary to use more than one Slater determinant to write the wave function of a quantum system?

Consider a system of $N$ non-interacting identical fermions of spin $s$, spin quantum number $m_i=m_{s_i}$and position coordinates $\mathbf{r}_i$. Let $\alpha$ denote a state specified by the numbers $...
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Can Aufbau principle be derived/proved with a definite reason? [duplicate]

How is Aufbau principle derived or proved? on a note, why does the energy of 3d subshell is More than that of 4s subshell, instead as 4s is greater in extent than 3d,4s should have greater energy! ...
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What carries the information for the Pauli exclusion principle to occur?

I have been reading about the exclusion principle a little bit, but I have some questions about it. How does the information about the state of electrons get "passed around" so that other ...
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Does Pauli exclusion principle put a limit on the number of overlapping fermions?

It seems there should be no limit to the number of electrons that can have overlapping probability clouds. They repel each other due to charge, but if there were some other force like gravity holding ...
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Free particle in quantum mechanics (Pauli principle?)

By what is a state of a free particle defined? For a bound electron for instance it is fully described by the quantum numbers $n,l,m$ and the respective state $|n,l,m\rangle$. But by what is the free ...
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Adding quantum numbers breaks exclusion principle?

Consider 2 non-interacting Fermions with spin $s\ne 0$ trapped in a 1D harmonic potential with ground state $\left|\phi_0\right\rangle$. Due the Pauli exclusion principle I would expect that only 1 ...
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