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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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Why are there no transitions between orthohelium and parahelium?

I know the transition rule $\Delta S = 0$. But where does that rule come from? Is it just very unlikely that an absorbed/emitted $\gamma$ will carry the energy necessary for a spin flip? Or is there ...
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Racah's Derivation of CG coefficients

I have what is hopefully a quick question. In Racah's 1942 paper Theory of Complex Spectra II, the author utilizes the action of $J_+$ on the Clebsch Gordan expression: $$ \begin{align*} &|j m\...
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Clebsch-Gordon Coefficient Recursion Derivation

I've got a question regarding a very particular recursion relation that Condon and Shortley use in their book "The Theory of Atomic Spectra," (TAS) which Racah then uses to derive the algebraic form ...
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Angular Momentum of Object Accelerating in a Straight Line [on hold]

I've been given an object with $r(t)=|v|t\hat{x}+b\hat{y}$ and been asked to find the specific angular momentum and see if angular momentum is conserved. I found $L=r\times p=-m|v|b\hat{z}$. My ...
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Hamiltonian in rotating frame

I have a Hamiltonian for spin in a magnetic field $$ \hat{H}(t) = \mathbf{B}(t) \cdot \mathbf{\hat{S}}$$ $\mathbf{B}(t) =B_x(t) \hat{\mathbf{x}} + B_y(t)\hat{\mathbf{y}} + B_z(t)\hat{\mathbf{z}}$ is ...
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Why we need $SU(2)$ symmetry? When we use it? [closed]

I am trying to learn Quantum mechanics and I am familiar with Pauli matrice but not with group theory. I want to understand SU2 symmetry in common language. When we talk about Pauli matrix x we simply ...
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Speed of the rotating block [duplicate]

Problem: A block tied to a string is rotating with an angular velocity $\omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the ...
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How is a perpendicular angular momentum origin in gyroscopic precession?

Assume in the given diagram, $\theta = 0$, for sake of simplicity Then, I understand there exists an initial angular momentum in the y-direction and a torque in the X direction of the gyroscope. This ...
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Why is angular momentum of the Earth/Moon system conserved?

Why is the angular momentum of the Earth/Moon system conserved, apparently unaffected by external forces such as force of the Sun?
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Conservation of angular momentum during rolling with slipping [closed]

A block of mass m moves with a velocity $\mathbf{B}$ on a smooth horizontal surface. It then passes over a cylinder $R$ and mass $m$, capable of rotating about it's own axis through $O$. The block ...
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Will the plate go back to its original position?

Assume there is a round plate whose moment of inertia is $I$ with regard to the axis cross its center, supported by a stick at its center. On the plate there is an insect sleeping at some point on the ...
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Explicit description of $\vert n,s,m \rangle$ states

I have $n$ electrons in $n$ different orbitals. Let $s$ be total spin and $m$ the z-componente of spin. $s$ can be any number between the minimum ($0$ or $1/2$, depending on parity) and $n/2$, and $m$ ...
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From spin representation of state vector to other representation

I have learned that the state vector (ket vector) can have many representations, and the laws of quantum mechanics give one the ability to change between representation. But there is a subtle point ...
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Is the right hand rule a trick to avoid tensors?

I have read in this answer that "to represent angular momentum as a vector you need to use a right hand rule. This is annoying, because physics at ordinary scales is reflection invariant but ...
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Rotor why not opaque?

Helicopter rotors spin at around 300RPM. Now for the naked eye they look like transparent, like if the rotors were not even there. https://www.quora.com/Why-do-we-see-individual-helicopter-rotor-...
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If a gyroscope is provided a torque in space, what will its motion be after the torque ceases to act?

As there will be no energy dissipation, where will the kinetic energy of precession go as the gyroscope can't precess in the absence of a torque? Thanks in advance!
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Parity conservation in electromagnetic decays

When a $\pi^0$ decays into photons, the only possible number of photons to which it can decay is 2$\times n$, with $n$ a natural number. This is because in electromagnetic decays charge conjugation is ...
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1answer
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Tendency of rotation of an object in space [duplicate]

My teacher explained that when an external load is applied on an object in space ,eccentric to its centre of mass, the object will be accelerated linearly(along a straight line) because there will be ...
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Conservation of Angular momentum during inversion of a rotating wheel

in the picture the person is sitting with a wheel rotating. He just reverses the wheel so that the angular velocity and angular momentum too are inverted. Then according to conservation law the system'...
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Vector Spherical Harmonics and total angular momentum

In their book Akhiezer et al. give a definition of vector spherical harmonics (p.18 of Russian Edition) as $$\pmb{Y}_{j\ell m}(\pmb \Omega) = \sum_{m' \lambda} \langle \ell m' 1\lambda| jm \rangle Y_{...
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Putting the ket $|l,m_x \rangle$ in terms of the ket $|l, m_z \rangle$

Could someone guide me in my thought process of this problem? I don’t know if I’m thinking about it the right way. The problem is the following: I have a system which possible states are generated ...
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1answer
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Rolling point of contact [closed]

I have been reading "variational principles in classical mechanics" by Douglas Cline and the following page rather confused me. It states that for a cylinder rolling without slipping, the velocity of ...
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If a torque stops a wheel from spinning, will the wheel continue to move forward without spinning?

If a torque applied on a spinning wheel stops a wheel from spinning (on a horizontal surface) will the wheel continue to move forward without spinning?
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1answer
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In which scenarios is the derivative of mass moment of inertia ignored and taken into consideration for rigid bodies?

When taking the time derivative of Angular Momentum The first two terms represent the relative rate of change with respect to the coordinate system used. Most sources I have been reading state that ...
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Can a non-rotating ball have angular momentum?

Suppose a ball is going straight along a fixed line without rotating. Now you consider a point which is not along the trajectory of the ball. If I want to consider the angular momentum about that ...
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1answer
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Construct components of tensor operator [closed]

I'm reading Georgi's textbook on Lie Algebras and have been struggling with this question for quite awhile. The entirety of Chapter 4 (Tensor Operators) has been much more difficult than anything I've ...
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1answer
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What is the Lagranian correponding to this Hamiltonian?

The Hamiltonian is $$H=\vec{S}\cdot\vec{B},$$where $\vec{S}$ is spin, and $\vec{B}$ is external magnetic field. My question is what is the corresponding Lagranian?
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1answer
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Linear momentum conservation for interaction between rigid body and point mass

Let's say I have an interaction potential between a rigid body and a point mass expressed in spherical coordinate : $V=V(r,\theta, \phi)$. The coordinates $r, \theta$ and $\phi$ specify the position ...
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Angular momentum in Rotating Frame for satellites

I am working on satellite orbit propagator, I am propagating the satellite position and velocity in the inertial and rotating frames. To validate my propagator, I am checking the angular momentum and ...
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1answer
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Can electrons jump between levels in same shell with constant $L$?

I see many cases where electrons jump from various energy levels of some $L$ value to various levels of other $L$ value. But is there any transition in same $L$ level between its different ...
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Why do things spin?

Let's say I have 2 boxes, one of mass M and one of mass 2M. They are separated by a distance of 1 meter. I drop them from the same height and see that due to the earth's gravity, they accelerate at ...
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How is the product $L\cdot S$ between orbital and spin angular momentum operators defined? Do they act on the same or different Hilbert spaces?

For an electron, are the Hilbert spaces for the spin angular momentum and the orbital angular momentum the same or are they different? If they're different, how do we justify the operator $L\cdot S$ ...
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Conservation of angular momentum in a rod with hinge on one end

Consider the case a rod with hinge on one end in horizontal position. At the instant when it is released, the weight of the rod is going to give it a torque with an acceleration. Why is angular ...
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How do we know that the motion of the particle in an central force field lies on a plane?

If I take r as the radial vector of the moving object and v as the velocity vector of the moving object in central force field. Then r should be perpendicular to r×v . So that depicts that r.(r×v) = ...
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Angular momentum in merging stars

See taylor's classical mechanics page 302. where $E=T+V=\frac{1}{2}m\dot{r}^2+\frac{l^2}{2mr^2}+U(r)$ thus for a two body problem with angular momentum $\neq 0$ the objects could never come close to $...
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How to use Hund's third rule for excited electronic configurations?

Hund third rule states: For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number ${\displaystyle J\...
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Angular momentum conservation in Quantum Mechanics, how does it work?

In Classical Mechanics it is "easy", if some system has some angular momentum at the beginning then conservation of angular momentum means that no matter what happens, the angular momentum vector at ...
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Facilitated Circular Reflection

This question is a different take on my "Circular Reflection" question, which has been answered. Suppose a beam of light is made to travel in a circular path along the cross section of a transparent ...
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What is the meaning of angular momentum about a point? [closed]

Angular momentum is always calculated about an axis and not about a point( according to me). I have a scenario on this topic. In the image below it is asked to calculate angular momentum about origin....
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Total Angular Momentum of an odd-parity shell-model state with 4 nucleons

If an odd-parity shell-model state can hold up to a maximum of 4 nucleons what are its values of J and L? Total angular momentum, J, is equal to orbital angular momentum, L, plus spin, S. J = L + S ...
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What's the difference between rotational Energy/angular momentum and linear kinetic energy/linear momentum?

Consider the point mass $M$ being hold by a massless string at distance $r$ and rotate at angular frequence $w$. Energy: To orter to obtain the energy of the point mass, we calculate as a rotational ...
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Circular Reflection

How efficiently can light be turned into angular momentum? Light can be contained for long paths via total internal reflection with some steady decline in intensity due to absorptivity of the medium. ...
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1answer
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Would a Lunar space elevator only be stable if it passes through Earth-Moon L1 or L2?

I understand that space elevators are extremely hypothetical (bordering on pure fiction), but they are supposed to be theoretically possible. My questions is about what longidtudes a lunar space ...
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3answers
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Why are there three $p$-orbitals?

This question is specifically about Schrödinger quantum mechanics, but if an answer in some other mode would illuminate it could be acceptable, as demonstrating a physical or mathematical reason for ...
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5answers
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Why does an electron have spin? [duplicate]

An electron is assumed to be a point particle that does not have structure and volume. Why does it have spin? Does this imply that the electron has volume? It is hard to imagine that a point (without ...
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1answer
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Relation between acrobat and principle of conservation of angular momentum

How the principle of conservation of angular momentum is used by an acrobat to rotate a few revolution while leaping throung the air?
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1answer
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Spherical symmetry and mean of angular momentum

I have the following problem. Consider a 3 dimensional system with spherical symmetry. Consider a state $|\psi \rangle$ such that the possible results of a measure of operator $L^2$ (square of ...
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1answer
58 views

SO(3), orbital angular momentum, vector product

I have a big confusion with group theory terminology. I know that orbital angular momentum (OAM) is $\mathrm{SO}(3)$-symmetric in 3D-space. Let's define QM orbital angular momentum (OAM) ...
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1answer
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Time average value of Spin operator

From the book Introduction to Quantum Mechanics by Griffiths,. In the section 6.4.1 (weak field zeeman effect) Griffiths tells that the time average value of $S$ operator is just the projection of $S$ ...
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Does converting light's linear momentum into angular momentum (SAM or OAM) cause it to redshift?

Can all of an electromagnetic wave's momentum be changed to orbital angular momentum? I'd imagine this would be easier to test with radio waves.