Pauli Definition and 229 Threads

I have been reading through Mark Srednicki's QFT book because it seems to be well regarded here at Physics Forums. He discusses the Dirac Equation very early on, and then demonstrates that squaring the Hamiltonian will, in fact, return momentum eigenstates in the form of the momentum-energy...

As far as I know a Baryon is made of three Quarks (eg uud, udd etc) and a Meson of two Quarks, a Quark/Antiquark pair. As I am not a student / scholar in Physics but very deeply interested in this field, I couldn't find any explanation, why a Meson is omly made up by a Quark/Antiquark pair. What...

Where does the Stern Gerlach term in the Pauli equation come from? Taken from http://en.wikipedia.org/wiki/Pauli_equation. Following wikipedia's steps the Stern Gerlach term pops out when you apply the Pauli vector identity. I don't understand this step. It seems as if there should be no Stern...

If I understand correctly (no guarantee), the angles A and B in the generator of the three Pauli matrices (excluding the identity): cos A......exp(-iB) sin A exp(iB) sin A....-cos A refer to angles in a Hilbert space, for example the...

In a bosonic atom i.e. Hydrogen, why do we never observe quantum tunneling past the coulomb barrier leading to multiple atoms occupying the same area of space thus (due to Newton's law of universal gravitation) accelerating towards each other resulting in nuclear fusion?

In basic chemistry, we "fill up" the energy levels of an atom by putting two electrons in each energy level. The justification for this (that I've seen) is that the Pauli exclusion principle only allows one electron per state and there are two states in each energy level (spin up and spin down)...

Homework Statement Hi i've noticed that, J^{ab}P^c + J^{bc}P^a+J^{ca}P^b = 0 [ Since J^{ab}P^c + J^{bc}P^a+J^{ca}P^b = x^a\partial^b\partial^c -x^b\partial^a\partial^c + x^b\partial^c\partial^a-x^c\partial^b\partial^a+x^c\partial^a\partial^b-x^a\partial^c\partial^b = 0 ] Next, I tried it on...

I want to find a matrix such that it takes a spin z ket in the z basis, | \; S_z + >_z and operates on it, giving me a spin z ket in the x basis, U \; | \; S_z + >_z = | \; S_z + >_x I would have thought that I could find this transformation operator matrix simply by using the...

Homework Statement In the Pauli theory of the electron, one encounters the expresion: (p - eA)X(p - eA)ψ where ψ is a scalar function, and A is the magnetic vector potential related to the magnetic induction B by B = ∇XA. Given that p = -i∇, show that this expression reduces to ieBψ...

I've seen it stated in many places that the reason why atoms don't collapse is due to the pauli exclusion principle. The exclusion principle is given as a required anti-symmetry in the wavefunction of electrons. I don't understand how this principle was derived, or where it comes from. (I've...

I want to write a program that, given the tracked position of a cube being rotated, applies analogous operations to a single qubit. The issue I'm running into is that, although operations correspond to rotations on the Bloch sphere, the mapping isn't one-to-one. So when I try to map back to...

Homework Statement Find the matrix representation of S_z in the S_x basis for spin 1/2. Homework Equations I have the Pauli matrices, and I also have the respective kets derived in each basis. There aren't really any relevant equations, other than the eigenvalue equations for the...

I have a few questions about the Pauli exclusion principle: 1. Why do physicists believe that the symmetry in the wavefunction we assign to particles (indistinguishability) is due to an actual restriction in the physical state space that the particles can occupy (the attributes following from...

Homework Statement Prove \exp (\alpha \hat{\sigma}_z+\beta \hat{\sigma}_x)=\cosh \sqrt{\alpha^2+\beta^2}+\frac{\sinh \sqrt{\alpha^2+\beta^2}}{\sqrt{\alpha^2+\beta^2}}(\alpha \hat{\sigma}_z+\beta \hat{\sigma}_x) Homework Equations e^{\hat{A}}=\hat{1}+\hat{A}+\frac{\hat{A}^2}{2!}+...

I have a question: can the mechanism behind Pauli's exclusion principle be considered a fundamental force, like gravitational, electromagnetic, nuclear weak or strong? Why? Thx.

Can one deduce from Pauli's exclusion principle (through the Slater Determinant) that two electrons with different spins in the same energy level, can't have the same position?

I think this is more or less a quick question. So deuteron (pn) is an isosinglet in the state |00> =\frac{1}{\sqrt{2}}(pn-np) since it cannot be part of the isotriplet that includes pp and nn, since these violate pauli exclusion. That's fine. So how is it that we can have atoms like...

The 3s and 3p orbitals are filled by 4 electrons.A single atom has [Ne]3s2 3p2.But when multiple atoms get together they do so in order to minimize the overall energy.And to minimize the overall energy,the 3s and 3p orbitals hybridize to form 4 tetrahedral SP3 orbitals.And the Si atoms get...

Hi, I know this is old news at this stage, but I was watching his public lecture on quantum mechanics, and he says the energy levels of all the electrons in the universe shift to adjust when he adds energy to electrons in a diamond. I understand that he should have used the phrase quantum...

Hi New to this forum. I am not a physicist (maths :confused:), but have a healthy curiosity and interest in Quantum physics. I have a question regarding the Pauli Exclusion Principle. From what I have understood previously, this applies to a single atom or maybe atoms in close proximity...

Hi. New member to this Physics forum and not a physicist, although have an interest in physics from a layman's position. I saw a series of threads on a Twitter discussion posted about a year ago concerning Brian Cox and some other physicists concerning a statement made by Cox that the...

Homework Statement Whats up guys! I've got this question typed up in Word cos I reckon its faster: http://imageshack.com/a/img5/2286/br30.jpg Homework Equations I don't know of any The Attempt at a Solution I don't know where to start! can u guys help me out please? Thanks!

1. Consider the 2x2 matrix \sigma^{\mu}=(1,\sigma_{i}) where \sigma^{\mu}=(1,\sigma) where 1 is the identity matrix and \sigma_{i} the pauli matrices. Show with a direct calcuation that detX=x^{\mu}x_{\mu} 3. I'm not sure how to attempt this at all...

Hi, Wasn't sure if I should post this to Linear Algebra or here. My question is really simple: Can a 2N by 2N random, and Hermitian Matrix ( Hamiltonian ) be always written as: H = A \otimes I_{2\times 2} + B \otimes \sigma_x + C \otimes \sigma_y + D \otimes \sigma_z where A,B,C,D are all...

Hi everyone, I'm going through some lecture notes on Quantum Field Theory and I came across a derivation of an explicit form of the Pauli Jordan Green's function for the Klein-Gordon field. The equations used in my lecture notes are equivalent to the ones in...

Some time ago I asked about contact forces and was directed to read about the Pauli exclusion principle and the resulting L-J potential before a detailed explanation was given explaining why the electrons start interacting significantly, electromagnetically, even if the atom as a whole is...

When a fermion x approaches another fermion y does x send out bosons to y which tell it to get out of the way? In short, how does y know to get out of the way of x?

Homework Statement Express the product where σy and σz are the other two Pauli matrices defined above. Homework Equations The Attempt at a Solution I'm not sure if this is a trick question, because right away both exponentials combine to give 1, where the result is...

Hi, I think I need a sanity check, because I've been working on this for a while and I can't see what I'm doing wrong! According to several authors, including Sakurai (Modern QM eq 3.3.21), a general way to write an operator from SU(2) is...

I've recently had the oportunity to read the fantastic work Wolfgang Pauli did to summarize the theory of relativity for an encyclopedic article and I have a question about the final part of the article where Pauli addresses the problems of the theory to ultimately solve the problem of the...

Homework Statement Q1. Briefly explain the relevance of the Pauli exclusion principle for the structure of the periodic table of the elements. Q2. What is the maximum number of electrons that can be located in an atomic subshell with quantum numbers n and L? Briefly expain your answer...

Why are the Pauli matrices multiplied by 1/2 ?? Why are they represented as σ1/2 σ2/2 and σ3/2 and not just σ1 σ2 σ3 ?

Deuterium atom is an isotope of hydrogen [NP]e- that is a fermion. Would it be correct the model the deuteron [NP] nucleus as a boson, given that it has even number of particles ? That is, would it be correct to say that two deuteron [NP], as bosons, could occupy the same particle state...

Show that all hermitian 2x2 matrices with trace 0 are elements of three dimensional vector space in \mathbb{R}, which basis vectors are Pauli spin matrices. Any clues on how to begin? :/

I was told that the pauli exclusion principle states that no two electrons in an atom can have the same quantum numbers is it ture need answers!

I'm studying fermions with one of Leonard Susskind's video courses. The Pauli Exclusion principle seems odd and counterintuitive. My question is this, if I learn enough quantum theory will I learn why Pauli Exclusion exists; not just how it works? Does the Pauli Exclusion principle pop out...

How do fermions, which have vast amounts of empty space, know not to occupy the same space as another fermion? Do physicists say that the two fermions become entangled and that is what enables them to be "aware" of the "existence" of the other fermion? Is entanglement used as an explanation...

This is a question I've had for some time now. Why is the exchange interaction not considered a force, like the other 4 fundamental forces? When reading solid-state physics texts, for example, I come across explanations of this kind: the atoms cannot get too close together because of the...

Hey all, I have what I think (hope) is a relatively quick pair of questions regarding entanglement of fermions and bosons. First, am I right in saying that if two fermions are in the same position-state, they will necessarily be entangled? My reasoning here is just that if their...

Homework Statement Which of these particles don't follow Pauli exclusion principle and thus have a symmetric wave function? a) Bosons b) Fermions c) Quarks d) All particles follow Pauli exclusion principle Homework Equations None. The Attempt at a Solution I think that...

Homework Statement Pauli Spin matrices (math methods in physics question) Show that D can be expressed as: D=d_1\sigma_1+d_2\sigma_2+d_3\sigma_3 and write the d_i in terms of D's elements, let D also be Unitary Homework Equations - Any 2x2 complex matrix can be written as ...

Homework Statement

Hello, I am new to this: Taking the first Pauli Matrix: σ1=[0 1 1 0] Doing the transpose it becomes: [0 1 1 0] So is it a unitary matrix? Similarly σ2= [0 -i i 0] Doing a transpose =[0 i [-i 0] Does it mean the complex conjugates are...

Hello! I have two questions regarding QM. First, I tried to rotate J_z into J_y for the j=1 representation by the transformation rule for matrices.. I took my rotationvector to be (1,0,0) and rotated about 3/4 pi radians which I thought would give me S_y. Instead I got S_z again! Wolfram...

Hello I'm reading my old notes of QM, I found the definition of Pauli vector, as follow \vec{\sigma}=\sigma_1 e_x+\sigma_2e_y + \sigma_3 e_z Where e_x. e_y and e_z are unit vectors. So, here is my question. \sigma_i and e_i are elements of different nature. How can we define the product...

Why must we apply the Pauli Principle to electrons in a metal? Do they share a many-body wavefunction? The saying is that no two electrons may occupy the same state, but am I allowed to say "well, this electron is at the top of the metal, and there is another one at the bottom, those two are...

In the article, "What is spin", by Hans C. Ohanian we are shown how to take the wave-function for a Dirac electron with spin up and localized in space and then determine the momentum density in the Dirac field. The momentum density divides into two parts, a part that depends on the motion of the...

The earliest instance I've seen to this equation, involving the Pauli matrices, is from a 1967 paper by J. M. Levy-Leblond. But it seems general and useful enough that it must have been discovered earlier: (\sigma \cdot A)(\sigma \cdot B) = A \cdot B + i \sigma \cdot (A \times B)

How was Pauli exclusion principle derived ? Experimental ? From some other physical formula ? Which ? From some other principle ? thanx

Curious about the wave functions of elections shared in covalent bonds. If you have two hydrogen atoms w elections in the lowest energy state with the same spin and they join together to form a molecule H2 The spin of one of the elections will change (randomly?) The electons of the two...