Questions tagged [angular-momentum]
The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation
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If the electron were not precessing would its spin along $z$ be $√3/2$ instead $1/2$? [closed]
If the electron were not precessing would its spin along z be √3/2 instead 1/2 as the number √3/2 is the total spin which is somehow shared by x,y and z axis? Should this precession causing an ...
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Translation of generators when derive representations of Poincare group on fields
As stated in section 4.2.1 of Di Francesco's book on conformal field theory. In order to find out representation of Poincare group on fields, we can start by studying the subgroup that leaves the ...
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Trouble understanding portion of derivation of relative motion in two-body problem
I'm doing some self study using Prusing and Conway's Orbital Mechanics. In the first chapter there is a derivation of r for relative motion that I'm having a little difficulty following. Specifically, ...
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Has the “spin” of a photon anything to do with a rotation movement?
If not, where does this denomination come from?
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What is the momentum lost every time it swings? [closed]
If you swing a pendulum, every time the pendulum swings, how much momentum is lost, is it based on the size of the string it swings on, the mass of the object, or what formula is it?
No friction
The ...
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Relation between Clebsch-Gordan Coefficients and Wigner $D$-Matrix
It is known that Clebsch-Gordan coefficients are those of a linear transformation from the product basis $\{|j_1,j_2;m_1,m_2\rangle\}_{m_1\in \{-j_1,...,j_1\},m_2\in \{-j_2,...,j_2\}}$ to the coupled ...
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Eigenstates for $\vec{L}^2, L_z, L_x$ and $L_y$? [closed]
I am asked to find states $|j,m\rangle$ that are simultaneously eigenstates for $\vec{L}^2, L_z, L_x$ and $L_y$. I know that the $L_i$ operators do not commute and hence you cannot have a state $|\phi\...
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Why can't we use conservation of angular momentum to solve this question since this whole system is isolated?
A solid rubber wheel of radius $R$ and mass $M$ rotates with angular velocity $\omega_0$ about a frictionless pivot. A second rubber wheel of radius $r$ and mass $m$ also mounted on a frictionless ...
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Is muon a point particle? [duplicate]
Im just a beginner in particle physics. As I have understand, electrons are considered as a point particle whose spin has nothing to do with original rotation around own axis but an intrinsic quantum ...
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Angular momentum in movement along a straight line
Angular momentum is conserved when no external torque is applied, I've learned that a long time ago and know the derivation. Yet, I've now been wondering about the following case:
Let's consider a (...
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Matrix representation of the $x$-component of orbital angular momentum $\hat{L}_x$
In my notes it is given that using the spherical harmonic (shown below) as basis states in this order, the matrix representing the $x$-component of orbital angular momentum $\hat{L}_x$ for a particle ...
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Gyroscopic Torque
I was going through this problem in which there was a disc mounted at one end of the rod and the other end of the rod is hanged using a rope. The disc is given angular velocity counter-clockwise. Now ...
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Rotation operator on $\lvert l, m\rangle$ state
Recently I came across Tensor operators and Wigner Ekart theorem , in one its derivations it was given that
$ \langle l',m'|\mathcal{D}_R |l,m\rangle = \delta_{ll'} D_{mm'}^l(R)$ .
Can I get an idea ...
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The degeneracy of spherical harmonics
On page 336 of Shankar's 'Principles of Quantum Mechanics' the author states "The $Y_l^m$ functions are mutually orthogonal because they are nondegenerate eigenfunctions of $L^2$ and $L_z$, which ...
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Geometric visualization of addition of angular momenta
Introduction
Consider the Hilbert space of two $\frac{1}{2}$ spin particles (electrons, for instance), spanned by
\begin{equation}
{|\alpha\rangle, \, \alpha = \uparrow,\downarrow}
\end{equation}
\...
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Apparent violation of the law of conservation of angular momentum in the torques experienced by two interacting electric dipoles
Question
Consider two dipoles $({p_1}\hat{i}$ and ${-p_2}\hat{j})$ kept in the $x-y$ plane at $(0,0)$ and $(d,0)$ respectively. Calculate the torque about the COM.
Approach 1
Suppose we select the COM ...
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Lower spin than one half? Spin other than whole/half integer? [duplicate]
Someone asked me to explain why spin can't be lower than one half. All I could say was field geometry, that it's the minimum non-zero twist in a particle's field. Is that right?
The follow up question ...
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Can you recover the quantum numbers from just the shape of the spherical harmonic?
So I was wondering, in quantum physics beautiful graphs are introduced displaying spherical harmonics relying on the quantum numbers of $m$ and $l$. But is it possible to recover these quantum numbers ...
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Finding neutrino's spin from beta-decay
Since in a beta decay
$n \rightarrow p+e^-+\overline\nu$
total angular momentum must be conserved
$\frac{1}{2}=s_p \oplus s_e \oplus s_\nu \oplus L$
it follows that for $L=0$ neutrino's spin is either
...
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What are the possible orbital occupation for a triplet state?
I am trying to run some Hartree fock calculation for interaction between an atom and a molecule. The molecule is in its triplet state and i have to indicate the orbitals that these unpaired electrons ...
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Finding the angular momentum of a rotation body w.r.t. a point on the body itself
We have to find the angular momentum of a rolling disc about the point P on the disc but when we taking point how do we think of relative rotational and translational motion about that point on disc .....
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Finding the lowest ground state of $\rm Ne$ spin-3/2 [closed]
enter image description here
The hypothetical configuration is $(1s)^4(2s)^4(2p)^2$.
However, I do not understand why $p=1$ is antisymmetric in this case. The solution I have uses the 1x1 C-G ...
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Is the velocity taken as zero at $t=0$ always?
For example if I place a block (at $t=0$) on a disc which is rotating about its axis, should I consider the velocity of block as zero at $t=0$? Or will it have some velocity at $t=0$ as it is placed ...
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What does the notation $^1 S_0$ represent in particle physics?
I'm coming across the notation $^1 S_0$, $^3 P_1$, $^1D_2$ etc. in relation to particle states. What do the two numbers and the letter represent? I've tried googling to no avail and it just appears in ...
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A question about angular momentum and angular velocity of a symmetrical body
I know that a symmetrical body rotating round a fixed axis, at a constant angular velocity, has the vector angular momentum and the vector angular velocity parallel, but if the angular velocity isn't ...
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Bohr's quantization of angular momentum
I cannot seem to find a derivation for $L=\frac{nh}{2\pi}$ I do not understand what led Bohr to quantize angular momentum in units of Planck's constant and how he was sure it works. I understand that ...
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Proving the rate of change of angular momentum about CM is equal to total external torque about CM
I've been going through Taylor's Classical Mechanics book and I have to use the result:
$$\sum m_{\alpha} \bf{r}_{\alpha}' = 0$$
where $\bf{r}_{\alpha}' = \bf{r}_{\alpha} - \bf{R}$, $\bf{r}_{\alpha}$ ...
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Why is angular momentum $mvr$ and not $mvr^2$ or $mvr^3$?
We know angular momentum $L = mvr$, where $v$ is the velocity in the direction perpendicular to the distance from the source to the object whose $L$ we are trying to measure. My question is why $L$ ...
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Quantum Central Force Problem and Angular Momentum
I am currently studying the quantum mechanics of the hydrogen atom. We have a proton and an electron orbiting around, so the Hamiltonian is:
$$H=\frac{p_1^2}{2m_1}+\frac{p_2^2}{2m_2}+U(|\vec{r}_2-\vec{...
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Why does a yo-yo bounce back up after reaching its full extension?
When a yo-yo that has a string wrapped tightly around its axle reaches its full extension, it automatically bounces back upwards, the string re-winding in the process. What causes it to do that? I ...
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Spin in Lorentz group and Poincare group
I am currently learning representations of Lorentz group and Poincare group by Harald's Introduction to Supersymmetry Chap.1. I have 2 questions about the definition of spin.
Provided that finite ...
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Physical interpretation of raising and lowering operators in Spin-1
when discussing a quantum harmonic oscillator I understand that the annihilation and creation operators are interpreted as removing or adding a photon to your oscillator. However, for a spin-1 system ...
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How do you calculate the forces acting on the axis of a physical pendulum?
I need help to calculate the forces F1 and F2 of this physical pendulum consisting of a rigid and homogenous rod with length l.
I have found the following equation using the law of angular momentum:
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Real concept behind bending of a cyclist while taking a turn
I am a high school student and I am very confused in a concept:
I came to this problem of bending of a cyclist while taking a turn , in the book that angle is calculated from the frame of reference of ...
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Clebsch-Gordan ambiguity not sign-related?
I'm learning to compute Clebsch-Gordan coefficients. For $j_1=1, j_2=1/2, j = 3/2$ and $m=1/2$ I got $$ |3/2, 1/2, 1, 1/2 \rangle = \sqrt{2/3} |1,0,1/2,1/2\rangle + \sqrt{1/3} |1,1,1/2,-1/2\rangle$$
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Conservation laws for the collision of two classical particles
In Kleppner and Kolenkow's An Introduction to Mechanics (3rd ed.), the authors state (p. 227) that for the collision of two classical particles with no external forces or torques, with 6 unknowns (the ...
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Is there a way to prove that different angular momentum components anticommute without using a specific matrix representation?
I know spin-1/2 Pauli matrices satisfy the anticommutation relationship $\{\sigma_i, \sigma_j\}=2\delta_{ij} \mathbb{I}$. I wonder how this can be proved without writing down the matrix representation ...
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Angular part solutions of Schrodinger's equation
Hello Physics Community
i'm trying to solve the angular part of Schrodinger's equation, specifically the $\theta$ part ,
$$
\left[\sin \theta \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\...
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Describing a subspace of a Hilbert space of $N$ spins 1/2
Consider having $N$ spins $1/2$, so the overall state of $N$ particles can be described by the total spin value $S=0 \ldots N/2$ (let us set $N$ to be even for simplicity), and the projection of the ...
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Question about the procedure to find eigenvalues for angular momentum in QM
I am reviewing griffiths QM explanation of Angular momentum, and when finding their eigenvalues he uses a ladder approach. He states that there has to be a "top rung", where
$L_+f_t=0$, and ...
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Why does the Dirac beta matrix commute with the angular momentum operator?
This is the Dirac Hamiltonian,
and Beta is
The question says it all, I don't understand why Beta would commute with $ \hat L$
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About the calculation of the Spin-orbit correction for the Hydrogen atom
I'm using first order perturbation theory to calculate the energy corrections due to the fine structure of the Hydrogen atom. I'm having some doubts about the calculation of the spin-orbit term. Some ...
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Eigenvalues and eigenstates of $\hat{L}=\sqrt{\hat{L}^2}=\sqrt{\hat{L}^2_x+\hat{L}^2_y+\hat{L}^2_z}$ (without squaring)
I know that $$ \hat{L}^2 \left| l,m \right> = \hbar^2 l (l+1) \left| l,m \right> .$$ Does this mean that $$ \hat{L} \left| l,m \right> = \hbar \sqrt{l (l+1)} \left| l,m \right> ? $$ If so, ...
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Modified Spectroscopic Notation (Shankar)
In Shankar's Chapter on addition of angular momentum in his Principles of Quantum Mechanics (Chapter 15 of the 2nd edition), he includes the section attached after describing the basic strategy for ...
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Derivation of formula in Theory of Complex Spectra. II of Giulio Racah
In this article Theory of Complex Spectra. II Giulio Racah defines $f(m_{1} m_{2} ; jm)$ by
\begin{multline}
\left(m_{1} m_{2} \mid j m\right)
=(-1)^{j_{1}-m_{1}} f\left(m_{1} m_{2} ; j m\right)\left[\...
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How come I can spin an object attached to a string as centripetal motion without slanting?
Using a free body diagram, on an object spinning in the air while attached to a string, there would be the force of gravity on the object and the tension force from the string. In centripetal motion, ...
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Is eigenfunction for angular momentum operator is unique?
I want to know if the commutation relation for angular momentum, $$\left[ J_\alpha,J_\beta\right] = i\hbar\epsilon_{\alpha\beta\gamma}J_\gamma$$
is enough for defining its unique eigenstate of spin, $\...
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Is angular momentum conserved in $e$-$e$ scattering?
Consider the collision of two electrons. Naturally, these two charges will exert and equal and opposite force on each other causing scattering.
Jackson and others calculate the energy loss due to this ...
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Representation theory of $SU(2)$ and half-integer eigenvalues
I'm reading "Symmetries and Standard Model" by Matthew Robinson. On pages 88-91, the author shows the representation of $SU(2)$ will in general have $2j+1$ states:
However, I don't quite ...
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Can we conserve Angular Momentum about a moving axis?
In this question, I encountered a problem that if we were to conserve angular momentum about a stationary point lying on the middle axis and then conserve it from the frame of Center of mass of the ...
