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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Physical difference between $\vert S=0, m = 0 \rangle$ and $\vert S=1, m = 0 \rangle$? [closed]

In context of a two spin $\frac{1}{2}$ particle systems, we know that, $\vert S=0, m = 0 \rangle = \frac{1}{\sqrt2}(\vert\uparrow\downarrow\rangle - \vert\downarrow\uparrow\rangle)$ $\vert S=1, m = 0 \...
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Parity of quantum numbers of combined system of two spin-1 particles

I'm looking at the following problem: Two identical particles of spin $1$ have centre of mass at rest. The particles have combined spin $\mathbf{S}$, relative orbital angular momentum $\mathbf{L}$ ...
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Where is the reaction force of an object that has just flung out from a circular motion?

An object in a circular motion will fly out tangentially when released. As per Newton's Third Law of motion, there is a reaction in every action. The moment the object is released, where is the ...
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Relativistic invariants of a classical field in 4D fashion: why the relation between the components of the current density holds?

I'm trying to understand how is justified the following relation between the first component of the current density integrated over the volume and the scalar product of the 4-vector current density ...
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Does the earth’s rotational angular velocity change?

This is what is written in The Feynman Lectures on Physics, Vol. 1 (ch.5) We now believe that, for various reasons, some days are longer than others, some days are shorter, and on the average the ...
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Help with conmutator identity with angular momentum and vector [closed]

I need to prove this identity: $ [ \textbf{J}^2, \textbf{J}\times \textbf{V}] = 2i\hbar( \textbf{J}^2 \textbf{V} - ( \textbf{J} \cdot \textbf{V}) \textbf{J}) $ Where $ \textbf{J}$ is an angular ...
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Need help with solution on a physics calculation involving newtonian mechanics - (angular momentum) [closed]

I have been looking into conservation of energy in association with angular momentum (or in simple terms perpetual-motion-machines). Specifically need an answer to the following - Let's say there is a ...
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Regarding linear momentum operator as vector operator

The vector operator $\hat V$ are defined as the vectors which satisfies the commutator, $$[\hat L_i,\hat V_j]=i\hbar\epsilon_{ijk}\hat V_k.$$ $\hat L$ is the angular momentum operator. Thus, if the ...
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Doubt tensor product states of bipartite system

Consider a system $A$ whose basis states are $|\phi_1\rangle_{(i)}\in H^{(1)}$ and a system $B$ whose basis states are $|\phi_2\rangle_{(j)}\in H^{(2)}$. Then the basis states of the combined system ...
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Wavefunction with two different values at same point

Consider a particle on sphere. Its Hamiltonian in spherical polar coordinates is given by - $-\frac{\hbar^2}{2mr^2}\Big(\frac{1}{\sin\theta}\frac{\partial}{\partial\theta}\sin\theta\frac{\partial}{\...
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Eigenvalue problem of $L_z$

From Shankar's QM book pg. 313, the eigenvalue problem for $L_z=XP_y-YP_x$ in polar coordinates is $$-i\hbar \frac{\partial \psi(\rho,\phi)}{\partial \phi}=l_z\psi(\rho,\phi)$$ since $L_z=-i\hbar\frac{...
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How to derive the the asymptotic momentum of a classical electron after it is ionized by a strong laser field

I was reading a recent paper, Capture into rydberg states and momentum distributions of ionized electrons. N. I. Shvetsov-Shilovski et al. Laser Physics 19, 1550 (2009). which studies the ionization ...
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Angular momentum of child and swing system [duplicate]

when a child is riding a swing the angular velocity of the swing with respect to the point of suspension keeps on increasing (given that, the child is keep on swinging by his own). Who is providing ...
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Operators that are invariant under rotation

Consider a system described by state $|\psi\rangle(x,y,z)$. $\hat U_n(\theta)$ is an operator which rotates the wavefunction about an axis $n$ by an angle $\theta$ in positive direction. $|\psi\rangle(...
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How to prove $\exp(-\frac{i}{2} \theta (e.J)) = I \cos(\frac{\theta}{2})- i( e.J) \sin(\frac{\theta}{2}) $ [closed]

The following identity $(\boldsymbol a\cdot\boldsymbol J)(\boldsymbol b\cdot\boldsymbol J) = (\boldsymbol a\cdot\boldsymbol b) I + (\boldsymbol a×\boldsymbol b)\cdot\boldsymbol J$$\tag1$ is used to ...
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Questions on Peter Woit's Proof of the Clebsch-Gordan Decomposition Theorem

I am reading Peter Woit's book Quantum Theory, Groups and Representations, section 9.42 (a similar version can be found here). In the book he proved a version of the Clebsch-Gordan decomposition ...
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Scattering in Shallow Bound States - Suppression of Matrix Element

In Weinberg's Lectures on Quantum Mechanics, given the S-matrix $$S_{\beta \alpha}=\delta(\beta-\alpha)-2 \pi i \delta\left(E_\beta-E_\alpha\right) T_{\beta \alpha}\tag{8.8.4}$$ where $$T_{\beta \...
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Why rotation is not an observable?

I am literally new to these terms, I read this somewhere that "some operators are not observables such as rotation" . Is the statement correct? Can't we measure or observe rotational ...
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Do vortex rings have an intrinsic forward momentum? (Feynman lectures II.41)

I was going through Feynman's lecture vol.II, #41 about non-viscous fluid mechanics, and he makes a point that I do not understand. Towards the end, he discusses vortex rings (he takes the youtube-...
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Can we conserve angular momentum in pure translation motion?

suppose a block is moving on a surface with velocity v paraller to the surface. the surface is rough and is exerting some frictional force on block. consider the point 'O' in above image. since net ...
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If we had 4 spatial dimensions would Saturn have a spherical shell instead of a ring?

I am only speculating here, but since we have 3 spatial dimensions, it's conceivable why a flat disc would form around Saturn since the momentum in $z$ axis would be cancelled out over time and we ...
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Transformation of angular momentum operator as a tensor

I’m currently reading the book from Steven Weinberg on Quantum Mechanics and I’m struggling with the following. If V is some vector observable is rotated, then for a symmetry transformation there must ...
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Will two passing bricks in empty space induce rotation in one another?

Two identical rectangular bricks with mass $m$ pass each other anti-parallel in empty space with a constant velocity $v$. Say the smallest distance between them is $s$. Assume the bricks to be aligned ...
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Calculation of the Inertia of cylidrical weights fixed to a flywheel [closed]

I am required to calculate the inertia of a flywheel and was wondering if anyone could help me with calculating the inertia of cylindrical weights attached to the flywheel. I’ve attached a diagram to ...
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How does a particle have torque and angular momentum?

I'm aware similar questions have been asked, but I didn't understand the answers. Can a particle experience torque? What about angular velocity and/or acceleration? Assuming a particle is a body ...
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How to calculate $\nabla\cdot (|L_{\perp}| \vec{v})$?

Let's assume I know $\nabla\cdot (|L_{x}| \vec{v})$ and $\nabla\cdot (|L_{y}| \vec{v})$, where $\vec{v}$ is the velocity field and $L_x$ and $L_y$ represent classical angular momentum components in $\...
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Spin networks: are there forbidden orientations for some edges?

A vertex has $m$ ingoing and $n$ outgoing edges and we say that it is ($m+n$) valent. when i see the graphical interpretation of the intertwiners ($2 j$ lines are associated to an edge with spin $= j$)...
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What is an orbital singlet?

For Helium atom we know there are spin singlet and spin triplet state corresponding to $S=0$ and $S=1$. But what if the electrons are more than two and what does singlet mean for orbital degree of ...
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What does $|λ,μ\rangle$ mean in Dirac notation? [closed]

My guess is that it's shorthand for Ψλ,μ but I've never seen it written like this before. Here is the video in question discussing ladder operators with respect to angular momentum. At 12:24
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Can singularities' spin be related to the quantum spin of elementary particles?

We do know that black holes can and sometimes do have angular momentum, as described by the Kerr metric. Though I have not found anything about the description of the angular momentum of the contained ...
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Conservation of angular momentum in a linearly accelerated particle

The angular momentum of a linearly accelerated particle in an inertial systems in which the line of motion passes through the origin is $\vec{L}=m\vec{r}\times\vec{v}=0$. But if I move my system of ...
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Does the direction of angular momentum of a table fan different for two people standing behind the fan and in front of the fan?

Does angular momentum of a table fan depend on place of observation? What is its direction of angular momentum of a fan when I stand behind a table fan? In front of a table fan? And along the same ...
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Why is angular momentum involved in a spinning ball hitting another?

One ball has a certain velocity and is spinning. It hits another ball, and each have a certain friction constant which kind of roughly defines how their surfaces interact. Now, when I was in high-...
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Condition for an operator on a quantum Hilbert space to behave like vector

In QM we work with $H=L_2(\mathbb{R}^3)$ as a Hilbert space of square-integrable complex-valued functions. Now we define a special set of three operators $L_x, L_y, L_z$ by $L_i = \varepsilon_{ijk} \...
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Why can the orbital quantom number $l$ take on half integer values? [closed]

In Griffiths' "Introduction to quantum mechanics", the author shows in chapter 4 that the orbital quantum number $l$ can take on half integer numbers. This is shown using Dirac's lowering ...
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Does a star that is far from any galaxy tend to rotate slower?

I'm wondering whether the rotation of a galaxy and the buffeting of the gas and dust within it by light and stellar wind and pressure waves makes nebulae or gas clouds in galaxies have more angular ...
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Do stars lose spin angular momentum, to planets, radiation, or gravitational waves, or in some other way get a longer period?

A spinning star is throwing off stellar wind, and electromagnetic radiation, which might be carrying away angular momentum, so that the star loses angular momentum, and its angular momentum per unit ...
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Is spin angular momentum per unit mass AKA specific spin angular momentum used outside of quantum mechanics?

A siderostat is an object (a device, normally) that has a constant orientation with respect to the "fixed stars", or rather with respect to the distant galaxies. An example would be a ...
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Rotation of astrophysical black holes

It's usually stated that "astrophysical black holes are expected to have non-zero angular momentum, due to their formation via collapse of rotating stellar objects". In other words: rotating ...
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Total rotational energy of oval-shaped object [closed]

I am analysing the rotational energy of an oval-shaped ball (after taking a series of videos of a rugby ball bouncing), through the following 3 axes of rotation...: ...I calculated the angular ...
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Is spin of elementary particles same as the rotation of a planet? [duplicate]

By the word spin of elementary particle, one would imagine the particle to be rotating around its own axis, just like a planet rotates, but is it actually true? While spinning does an elementary ...
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Does a cylinder/cone being spun around on an arm have angular momentum?

This question comes after seeing a video about the SpinLaunch company and their "centrifuge" launch system. As shown in the basic illustration below, a "rocket" shaped projectile ...
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Prove that every component of angular momentum commutes with $f$

Let $f( \hat {\vec r} , \hat {\vec p} )$ be the any polynomial in variables $r^2, p^2 $ and $(\vec r \cdot \vec p)$. prove that every component of angular momentum commutes with $\hat f$: $[\hat L_k ,...
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Why is climate change triggering faster rotation?

On July the 29th 2022, the Earth finished its rotation about 1.5 milliseconds earlier than the entire 24 hours. Scientists link this to climate change, saying that a possible reason could be due to ...
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Ballerina Universe Paradox [closed]

Imagine a ballerina spinning with angular velocity $\omega$ on the ground, you will see her arms opening due to the centrifugal force. Now think of the same ballerina but she is the only thing in the ...
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The proof of the Wigner-Eckart theorem for irreducible tensor operators

I am reading through Wu-Ki Tung's Group Theory in Physics and I met a problem when going through the part of the Wigner-Eckart theorem for irreducible tensor operators. In the 4.3 part of the book, ...
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Tong QFT Problem set 2, question 6: Normal ordering of angular momentum operator

I've been studying Tong's QFT notes and am trying to do problem sheet 2, question 6. here. We are asked to take the classical angular momentum of the field, $\begin{align} Q_i &= \epsilon_{ijk}\...
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QFT - angular momentum operator - follow up question

My question is a follow up to this question. I've been attempting the same problem and can't figure it out. In line 8, since $Ep$ and $Eq$ depend on $p$ and $q$ respectively, how did they move outside ...
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Addition of Two Elements of Group Representation (Quantum Mechanics angular momentum)

In Sakurai's Modern Quantum Mechanics I saw the author takes commutation of two infinitesimal 3D rotation matrices. He also claims that the Hilbert space rotation operators should satisfy the same ...
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Physical Intuition behind the products of innertia

Let's say a system of particles $(\alpha)$ is rotating around the z-axis, therefore $$\vec{L_\alpha} = m_\alpha (-x_\alpha z_\alpha w_z,-y_\alpha z_\alpha w_z,(x^2_\alpha+y^2_\alpha)w_z)$$ so $I_{zz} =...

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