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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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Commutator of $\hat {L}_x$ and $\hat{V}(\hat{r})$

Consider the angular momentum operator $\hat{L_x}=\hat y\hat{p}_z-\hat{z}\hat{p}_y$ and the potential operator $\hat{V}$ where the potential $\hat{V}=\hat{V}(\hat{r})$ is spherically symmetric. It ...
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Why is $L=0$ an allowed dipole selection rule for many-electron atom?

Why is $\Delta L=0,\pm 1$ are the allowed dipole selection rule for many-electron atoms but only $\Delta l=\pm 1$ for hydrogenic atoms?
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How come everything in the universe except the universe itself are spinning? [duplicate]

The planets and stars are spinning, galaxies and clusters are spinning so shouldnt the universe also spin? I think objects spin is to preserve angular momentum but it must also implied that in the ...
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How to generate a rotating electric field? [on hold]

Does it involve the use of any magnets? And if so is there a geometric centre where the resultant field is zero.
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Probability to get an Eigenvalue of Angular Momentum Operator on an Arbitrary Ket

Hello physics SE community, I am currently working on Principles of Quantum Mechanics by Shankar and i get stuck in page 336 (its not even an exercise). It basically said that "we may expand any $\...
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Gyroscopic Precession [on hold]

Two gyroscopes are made exactly alike except that the spinning disk in one is made of low-density barium, whereas the disk in the other is made of high-density gold. If they have the same spin angular ...
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2$\pi$ Rotation on integer vs half-integer spin states

I want to know how to get the following result: $$ e^{-i2\pi J_y / \hbar}|j, m\rangle = (-1)^{2j}|j, m\rangle $$ for an arbitrary spin state $|j, m \rangle$. What I've tried is to expand the ...
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Sci-fi ships falling on planets

I hope the question is suitable for this forum.... Watching Star Trek: The Next Generation, I have found at least a couple cases where a navigation malfunction on a shuttle makes it fall towards the ...
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Is spin 1 described by $SO(3)$ or $SU(2)$ [duplicate]

What spin is described by which rotation group? I always only find information about spin-1/2
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If positive particle Q is held at a fixed point, and a second particle is fired at it [closed]

If positive particle Q is held at a fixed point, and a second positive particle is fired at it. Would the angular momentum of the second particle constant? Why or why not?
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How does physics know something is spinning or rotating? [duplicate]

From a purely mathematical point of view, as far as I'm aware, there is no difference between rotating a singular point by a phase phi, using its own location as the centre, or rotating all but the ...
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Gyroscopic precession on a friction-less surface

I am having trouble understanding the total energy for a heavy spinning symmetric top (Gyroscope) on a friction-less surface. I am trying to understand it via the Lagrangian of the gyroscope. My ...
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For a rigid body, why we need to add angular momenta of all constituting particles to get the angular momentum of the whole body?

For a rigid body, We can define linear momentum of the whole system of particles by the definition of its centre of mass, ${\displaystyle \mathbf{R}_{cm}=\frac{1}{M}\sum_{i}{m_{i} \mathbf{r}_{i}} }$ ...
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Imagining zero orbital angular momentum for s-orbitals

Orbital Angular momentum of a s-orbital is always zero. One can easily imagine why this is so: QM says $\hat{p}=-i\hbar \nabla_{r}$, and since the s-wave functions are radially symmetric, the momentum ...
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Relation between irreducible representations and angular momentum in molecules?

The molecular Hamiltonian no longer commutes with the L square i.e. $ [\hat{H},\hat{L}^2]\ne0$ but it commutes with the symmetry operations of the molecular point group $G$ i.e. $ [\hat{H},\hat{R}]=...
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Operational definition of rotation of particle

The question in brief: what does it mean, operationally, to rotate an electron? Elaboration/background: I am trying to understand how representation theory applies to quantum mechanics. A stumbling ...
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Rotating object on table: from sliding to rolling

A object which is rotating around a horizontal axis is placed on a surface, and starts sliding (with kinetic friction). After some time, it starts rolling without sliding through the table. The goal ...
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How is Angular Momentum conserved about an axis on the road perpendicular to direction of motion for an ELECTRIC Vehicle accelerated on it?

Torque by friction is 0 and I don't find any other torque about this axis to increase the angular momentum of the Vehicle.
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Conservation of Momentum vs. Energy [closed]

If a mass $m$ travelling at velocity $v$ collides ideally with a massless shaft mounted on a massless bearing with an identical mass on the other end of the shaft: Conservation of momentum requires ...
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Which way does a cylinder on a slab roll after the slab is removed?

An article by Tokieda[1] begins: I lay a cylinder on a sheet of paper. I pull the sheet from under the cylinder, briskly or gently. When the sheet is pulled out, which way will the cylinder roll?...
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Is there a simple way to calculate Clebsch-Gordan coefficients?

I was reading angular momenta coupling when I came across these CG coefficients, there is a table in Griffith's but doesn't help much.
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Why do we get wrong answers for orbital angular momentum if we solve it algebraically?

It is a well-known fact that the values for the square of the orbital angular momentum of a particle $L^2$ and it's projection in the $z$-direction $L_z$ are $m\hbar$ and $l(l+1)\hbar$ and that $l$ ...
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QM question of the $z$ Matrix element in Angular Momentum Basis

I found a quite challenge quantum mechanics problem in a preparation sample test for a midterm. Consider an electron moving in a central potential. Suppose that we know the matrix element of the $...
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matrix elements of $\hat{z}$ operator under the angular momentum basis

I found a quite challenge quantum mechanics problem in a preparation sample test for a midterm. The sample test does not have a solution, so it is bothering. The question reads as follows: ...
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What maximizes angular momentum matrix elements?

Given a quantum particle in $\Bbb R^3$ with eigenstates $$\begin{align} \hat{h}\psi=& \;e \psi \\ \hat{h}\psi'=&\;e'\psi'\\ \dots\end{align}$$ I would be interested on the implications of $$...
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Zero uncertainity in components of angular momentum in Hydrogen atom

It is given that L and Lz,Lx,Ly commute.(L is total angular momentum, Lx is angular momentum along x axis). So, I can simultaneously know the value of let's say L and Lz. But, if I perform huge no of ...
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How to evaluate the matrix element of coulomb repulsion term between electrons in an atom suing spherical harmonics multipole expansion?

This is a lecture notes take from the following link on numerical calculation of atomic physics:http://www.phys.ubbcluj.ro/~lnagy/pdf/1curs.pdf I am trying to evaluate the two electron matrix element ...
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Does dimension of irreducible representations of the double cover $SU(2)$ of the 3D rotation group define spin of particle?

In quantum field theory, does dimension of irreducible representations of the double cover $SU(2)$ of the 3D rotation group conclusively define spin? In other words, Is spin 1 particle only thing ...
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Difference between the angular momentum for a mass following a trajectory and a mass rotating around a rotational center

I struggle to find a satisfying reason and formulation, why for a point mass, that is fixed in a rotational system and the radius is changed (like pulling on a string with a small ball rotating ...
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How can we prove the tensor-product basis $\{|j_1,m_1⟩|j_2,m_2⟩\}$ is linearly independent? [closed]

My reference is Walter Johnson's Book Lectures on Atomic Physics (2006). Given our coupled $J$'s in the equation bellow: $$m|j,m\rangle = \sum_{m1,m2}(m1 + m2)C(j_1,j_2,j;m_1,m_2,m)|j_1,m_1\rangle|...
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How to derive the formula of angular momentum of light in Maxwell equation?

According to wikipedia,the angular momentum of light is expressed by $$\epsilon_0\int \left(E\times \vec{A} + \sum_{i=x,y,z}\vec E_i(\vec r\times \vec \nabla)A_i \right) d\vec r$$ How to derive this?...
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Why do gas giants have similarly coloured stripes?

After looking at Jupiter and searching 'exoplanets gas giants' on google I found that many had stripes on them. I found that pretty peculiar. So why do they have stripes. I think it has something to ...
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Rod that is toppling over

A rod is about to fall over. If $N=mg$, then there is no resultant vertical force acting on the object. So how is the object able to fall over? Intuitively I understand why it would fall over but ...
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Why can't we expand the definition of the system until momentum is conserved?

So, here a ball initially moving with a velocity v and collides inelastically with a pivoted rod. I've learned that this is a classic example for the conservation of angular momentum. My question is ...
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Is angular momentum independent of axis (if axis is parallel)?

I have been told this is true for the moon on this question: Angular momentum of orbiting + rotating body but I don't understand why it should work. Surely the axis must be chosen such that the ...
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Clebsch-Gordan coefficient for 1x0

I'm trying to work out the combination of $|1\ 0 \rangle|0\ 0 \rangle$ (in this case they represent isospin, $|I\ I_3 \rangle$) using Clebsch-Gordan coefficients, but the table for $j_1\times j_2=1\...
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What is a good basis for this Hamiltonian with reduced symmetry?

What would be a good basis for a modified Hamiltonian that reads: $$ H_1 = \frac{1}{2}(L_+S_- + L_-S_+) + c_1 L_x + c_2 S_x,$$ from a symmtry point of view? The Hamiltonian itself is not difficult ...
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Integral formula for inertia tensor

Writing down the balance of angular momentum, we introduce the inertia tensor by the formula \begin{equation} J(t)a \cdot b = \int_{S(t)} \rho (t,x)\left( a \times \left( x - X(t) \right)\right)\cdot ...
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Angular momentum of a system about the center of mass

Let $\boldsymbol{R}$ be the center of mass of a system of particles. Then the angular momentum of the system is $$\begin{align} \boldsymbol{L} &= \sum \boldsymbol{r}_i \times \boldsymbol{p}_i\\\\ &...
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Confusion about angular momentum of earth moon system

My assumed definition of angular momentum is the sum over $i$ of $L_i =r_i\times{\omega_i}\times{r_i}$ for each particle about some origin. We have two spheres rotating about the centre of orbit. For ...
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Why is the parity of the spatial wavefunction $(-1)^{\ell}$?

Consider a composite particle state $|\psi\rangle$ (like a hadron or a meson) that is an eigenstate of some Hamiltonian (e.g. the QCD Hamiltonian). Since the Hamiltonian is invariant under rotations ...
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Angular momentum of orbiting + rotating body

Is the angular momentum of say the moon about the moon's orbital axis, equal to the sum of the angular momentum of centre of mass of the moon and the angular momentum of the moon about the orbital ...
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A question on a ballet dancer and her moment of inertia? [closed]

The classical example of conservation of angular momentum. I want to ask how we know that moment of inertia around center of mass change when in same time also center of mass change position? Why ...
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Dependency between centre of mass and toppling force; no hinge, force applied from centre

I'm a high school student taking the International Baccalaureate looking into the effects of the case when a force is being applied at the centre of the body, now this experiment does take into ...
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Rotational Motion, Kinematics, Air Resistance

When a body is thrown of height in a practical situation ( air is present ) considering air resistance is applying constant opposite force, we could calculate its speed by calculating acceleration ...
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Bohr's atoms model

Why might Bohr have been especially curious about the possible values of the angular momenta of electrons in quantum mechanics? What looks special about them?
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Derivation of Wigner $d$-matrix in terms of Jacobi polynomials

During my research I have come across the following identity $$ d^j_{m,m'}(\theta) = \langle j,m|e^{-i\theta J_y}|j,m'\rangle= \sqrt{(j-m')!(j+m')!\over(j-m)!(j+m)!}\left(\sin{\theta\over2}\right)^{m'-...
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In what cases (precisely) are Hund's rules valid?

I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the ...
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Elementary argument for conservation laws from symmetries *without* using the Lagrangian formalism

It is well known from Noether's Theorem how from continuous symmetries in the Lagrangian one gets a conserved charge which corresponds to linear momentum, angular momentum for translational and ...
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Angular Momentum Derivation without Vector products - is it possible? [closed]

I am trying to prove myself the formula for angular momentum: $$L = mvr = pr$$ without use of any vectors. I started by considering the comparison between $E = \frac{1}{2}mv^2$ and $E = \frac{1}{2}...