Pauli Definition and 223 Threads

A small part of my brain has been bugged by this for a while now, so I figured I'd ask. According to most teachings, as well as the wikipedia entry, there are only 4 fundamental forces. The strong and weak interaction, electromagnetism and gravity, and as far as I know the Pauli exclusion...

The Pauli equation (seen here) contains its spin dependence in the term which reads \frac{1}{2m}\left[ \sigma\cdot\left(p-\frac{e}{c}A\right)\right]^2 So let B be any vector. Then \left( \sigma\cdot B\right)^2 =\left(\sigma_1 B_1 +\sigma_2 B_2 + \sigma_3 B_3\right)\left(\sigma_1 B_1...

Is there agreement here or are all/most of the neutrons in the same state?

"More generally, no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously." Now a quantum state can be setup to describe a collection of atoms, or molecules, or the entire universe in one state. So my question is, two electrons in...

Homework Statement I'm supposed to derive the following: \left({\bf A} \cdot {\bf \sigma} \right) \left({\bf B }\cdot {\bf \sigma} \right) = {\bf A} \cdot {\bf B} I + i \left( {\bf A } \times {\bf B} \right) \cdot {\bf \sigma} using just the two following facts: Any 2x2 matrix can...

Hi, I'm trying to get to Pauli's equation from Dirac's equation in the weak field regime. Specifically, if I substitute \psi = \left(\begin{array}{cc}\chi \\ \varphi \end{array}\right) into the Dirac equation, I get two coupled equations i\frac{\partial\chi}{\partial t} =...

Can I check with someone - is the following pauli matrix in SU(2): 0 -i i 0 Matrices in SU(2) take this form, I think: a b -b* a* (where * represents complex conjugation) It seems to me that the matrix at the top isn't in SU(2) - if b=-i, (-b*) should be -i...

Does the 'Pauli exclusion principle' imply that the universe is only finitely creative? It's rather the philosophy than the physics behind it, I'm interested in. I just wanted to be sure I was interpreting this principle correctly. I thought it meant that there are only a discrete amount of...

Why is it that the Pauli spin matrices ( the operators of quantum spin in x,y,z) are the generators of a representation of SU(2)? I understand that we use the 2X2 representation as it is the simplest, but why is it that spin obeys this SU(2) symmetry and how is it that we come up with the Pauli...

Okay, I think everyone here knows what the principle states, so I am not even going over that. Is a proton not a fermion with is +1/2 spin? It has an half integral, hence it must be. However, how is this possible for a proton to be fermion when elements like gold have a lot of protons in the...

Hi, This might be an ignorant question but I have to ask it. The exclusion principle forbids particles from existing with the same quantum numbers, like, if you had 2 electrons, they have quantum numbers n, l, ml and ms, and one out of those 4 has to be different, right? What I was wondering...

According to this website, http://www.particleadventure.org/pauli.html "At one time, physicists thought that no two particles in the same quantum state could exist in the same place at the same time. This is called the Pauli Exclusion Principle, and it explains why there is chemistry." 1-What...

Dear All I'd be very grateful if someone could help me out with finding the trace of a product of 4 SL(2,C) matrices, namely: \mathrm{Tr} \left[ \sigma^{\alpha} \sigma^{\beta} \sigma^{\gamma} \sigma^{\delta} \right] where: \sigma^{\alpha} = (\sigma^0, \sigma^1, \sigma^2, \sigma^3)...

I'm trying to calculate the pauli-lubanski pseudo vector for different representations of the poincare group. The first rep is the infinite dimensional "angular momentum" rep where the generators of the lorentz part take the form : M_ab = x_a*d_b - x_b*d_a (for 3 rotations) M_ab =...

Hello. I was thinking. The collapse of a stellar nucleus into a black hole is an apparent contradiction to the Pauli exclusion principle, right? So which one of those theories fails at that point - quantum mechanics or the theory of relativity? I used to think that it's the theory of...

What happens when a neutron star collapses into a black hole and it's no longer obeying the Pauli exclusion principle? In terms of quantum mechanics? Say it collapses because it gets more massive. A "neutron degeneracy pressure" can be calculated, which is what keeps the neutron star from...

Hello, I am trying to recover the following calculation (where K,A are 4x4 matrices in SL(2,C)): --(start)-- "We expand K'=AKA^{\dagger} in terms of k^a and k'^{a}=(\delta_a^{b} + \lambda_a^{b} d\tau)k^b. Multiplying by a general Pauli matrix and using the relation...

In some text, I read something like this \vec{S}_i\cdot\vec{S}_j where \vec{S}_i and \vec{S}_j are "vectors" with each components be the pauli matrices S_x, S_y, S_z individularly. My question is: if all components of this kind of vector are a 3x3 matrix, so how do you carry out the dot...

I'm very confused By performing a lorentz transformation on a spinor \psi\rightarrow S(\Lambda)\psi(\Lambda x) and imposing covariance on the Dirac equation i\gamma^{\mu}\partial_{\mu}\psi=0 we deduce that the gamma matrices transform as S(\Lambda)\gamma^{\mu}...

Hi all, I am looking into the discussions of Pauli paramagnetism (arising from free neutral fermions with spin 1/2) in chapter 11.6 of K. Huang's Stat. Mech. (II ed) and in chapter 31 of Ashcroft and Mermin's Solid State Physics. It seems to me that these books do not agree on signs. So...

Homework Statement Suppose that [\sigma_a]_{ij} and [\eta_a]_{xy} are Pauli matrices in two different two dimensional spaces. In the four dimensional tensor product space, define the basis: |1\rangle=|i=1\rangle|x=1\rangle |2\rangle=|i=1\rangle|x=2\rangle |3\rangle=|i=2\rangle|x=1\rangle...

hi, I am studying the Higgs Mechanism these days. And I get two questions. I hope some ones could help me. 1>We know that due to the non-zero VEV, SSB takes place and higgs condensates give masses to bosons and fermions. I wonder that after the SSB and before the universe became as cool...

I know it's an area that mostly psychologists/cognitive scientists/neuroscientists are into. Wolfgang Pauli was certainly interested in psychology and of course there are the works of Penrose and Stapp on consciousness which no one knows what to make of. . . "The only acceptable point of view...

Hi everyone, I now able to understand spin matrix (if i am correct in other words Pauli matrix). For e.g., for S=5/2 systems the spin matrix (say for SX) is given by: Sx= 1/2[a 6X6 matrix] I hope members will know what is this 6X6 matrix! Since i don't know how to type matrix in this...

Homework Statement The Hamiltonian of an electron with mass m, electric charge q and spin of \frac{\hbar }{2}\vec{\sigma} in a magnetic field described by the potential vector \vec{A}\left( \vec{r},t\right) and a scalar potential U\left( \vec{r},t\right) is given by...

"older formulation of Pauli exclusion principle" Is there any old formulation of pauli's principle? If so, is it explain that "forbiding the presence of two electrons in the same quantum state"? I need that explanation.

Homework Statement Can anyone tell me why Pauli Matrices remain invariant under a rotation. Homework Equations Probably the rotation operator in the form of the exponential of a pauli matrix having an arbitrary unit vector as its input. It may also be written as: I*Cos(x/2) - i* (pauli...

If a star is sufficiently massive, neither electron or neutron degeneracy pressure will stop it from forming a black hole. How is Pauli exclusion principle reconciled with collapse to a singularity ? Since no two neutrons can occupy the same quantum state at the same time, how comes a...

In the textbook, it uses the pauli matrices to describe the spin and it will also form a vector \vec{\sigma} = \sigma_1 \hat{x} + \sigma_2\hat{y} + \sigma_3\hat{z} But each component, \sigma_i, i=1,2,3 is a 2x2 matrix. I am really confuse about the relation between \sigma_i and the...

I have some questions about Pauli matrices: 1. How do we calculate them? Which assumptions are needed? Are the assumptions related to properties of orbital angular momentum in any way? 2. How do we prove that the Pauli matrices (the operators of spin angular momentum) are the generators...

I have a question in my book where five electrons are placed in a infinite square well and I am supposed to calculate the lowest energies. My problem is with the electron configuration. I think that the first two shall be placed in n=1 and then the rest shall be placed in n=2. This since l=0,1...

Hey folks, I am trying to generate the Pauli matrices and am using the following formula taken from http://en.wikipedia.org/wiki/SU(3 ) "In the adjoint representation the generators are represented by (n^2-1)×(n^2-1) matrices whose elements are defined by the structure constants"...

hi i just wanted to ask if anyone could help me understand this principle i have read around and still seem to be getting nowhere. i found this example but its confusing and does not give explanations http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html#c1 thanks

Not really a specific homework problem, more of a conceptual problem that is going to come up again and again in problems: OK, I understand the physical interpretation of spin and magnetic quantum number, so much as we can give one. That is, m_s = the component of s (or is it s^2? oh...

OK, I understand the physical interpretation of spin and magnetic quantum number, so much as we can give one. That is, m_s = the component of s (or is it s^2? oh, dear...) in the arbitrarily chosen z direction. Specifically, I am looking at Griffiths, p. 155-157. The eigenstates for spin...

This has been bugging me for a while, but feel to tell me if it's a nonsensical or silly question.. Suppose there were 4 spatial dimensions instead of 3. How would we go about constructing the Pauli matrices? Assuming each matrix still only has 2 eigenvectors, we require 4, 2x2 mutually...

Pauli exclusion principle say that no two electrons can occupy the same state. But what would happen if we force them to occupy the same states?

If it takes energy to squeeze matter, then its a force at work right? And what is spin? I can put the quantized nature of spin in the back of my mind for a moment, but what the heck does spin do?

I remember reading about charge independence; about how the energy levels of mirror nuclei (correcting for differences in the colomb term) are identical… I think this suggests that the force between any two nucleons is the same, so the attraction of neutron-proton=proton-proton=neutron-neutron...

So two identical fermions can't occupy the same quantum state. But if one is same except higher in energy then the quantum wave pattern is different so can occupy the same space. Are there any values on the amount of energy needed to make two neutrons exist in the same space? I'm doing a...

Homework Statement If P^ is the momentum operator, and σ^ are the three Pauli spin matrices, the eigenvalues of (σ^.P^) are (a) (p_x) and (p_z) (b) (p_x)±i(p_y) (c) ± |p| (d) ± (p_x + p_y +p_z) Homework Equations The Attempt at a Solution Pauli matrices are related to rotation.So...

Having looked into neutrinos and the process in which they were found I've started looking more in Wolfgang Pauli himself. I've read into this principle but there are a few things I would like to clear up. I have picked out the information I am interested in learning abou. "The Pauli exclusion...

I've just been reading my notes on quantum mechanics and got to the Pauli exclusion principle. The way it was explained makes no sense to me. It says "no two identical fermions can be in the same quantum state". Surely there are some restrictions to the applicability of this statement? It...

We know that two particles can't exist in identical quantum states in the same place, fair enough. However, no particle can be sitting directly on top of another to infinite precision. Therefore, you can always say they're some minimum distance away from one another. Now suppose you have...

For years, I've taken the Pauli principle for granted, but now that I've taken a course on Subatomic Physics, I'm mystified again. The example is given in the course of Neutron Stars. Neutron stars are burning stars that experience an incredible compression, drawing a lot of matter in a very...

Pauli Exclusion Principle--question According to the Pauli Exclusion Principle, two identical FERMIONS cannot coexist in the same energy level within a nucleus. My question is, could two identical fermions coexist if they had opposite isospin, that is, does isospin make the two otherwise...

hey all, posted this before but no one managed to get it? question off a past paper that it can't do.../ state pauli exclusion principle (can do that) and explain its consequence in an atom (can do that). Use it to determine the values of n, l ml and ms of 10 neon atoms placed in a box at...

Usual way of expressing pauli exclusion principle is, that the two identical fermions must be on different states. This seems a confusing statement, since the meaning of the term "different states" isn't very clear. Suppose I have two electrons, otherwise in the same states, but other one being...

I need to show: (\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b}) where a and b are arbitrary vectors, sigma is the pauli spin operator. I was just wondering what the dot product...

Back in 2002, Lubos Motl wrote a paper on Title: An analytical computation of asymptotic Schwarzschild quasinormal frequencies Lubos Motl, Adv.Theor.Math.Phys. 6 (2003) 1135-1162 Recently it has been proposed that a strange logarithmic expression for the so-called Barbero-Immirzi parameter...