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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Angular momentum in string theory

Since strings are extended objects, is all angular momentum in string theory essentially "orbital" angular momentum? Or is there still a kind of intrinsic angular momentum assigned to a string? ...
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61 views

What is the difference between the process in which energy converts to matter and that in which it converts to antimatter?

What is the difference between the process in which energy converts to matter and the process in which it converts to antimatter? In colliders, for instance, is the product (either being the matter or ...
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3answers
251 views

If space and time are equivalent, what's Spin in time dimension

This troubles me: We are talking about time and space being equivalent, but still only consider Spin in the $x$, $y$ or $z$-direction. What's Spin in time dimension? Is it distinction between ...
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1answer
339 views

Holstein-Primakoff and Dyson-Maleev representation

In Holstein-Primakoff and Dyson-Maleev representation, spin operators are represented by bosonic operators. Roughly speaking, a state with $S^z=S-m$ corresponds to a state containing $m$ bosons. In ...
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661 views

Angular momentum operator in terms of ladder operators

I wanted to show that the angular momentum of the particle state with zero momentum $| \vec{0} \rangle$ is $0$, that is to say the intrinsic spin of a scalar field is $0$ using a mode expansion. There ...
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404 views

Why does optical pumping of Rubidium require presence of magnetic field?

The optical pumping experiment of Rubidium requires the presence of magnetic field, but I don't understand why. The basic principle of pumping is that the selection rule forbids transition from ...
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5answers
555 views

What happens to angular momentum when matter is converted to energy?

Let's say a spinning star radiates mass-energy only from it's pole regions. How does the loss of mass-energy effect the angular momentum of the star?
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573 views

How do you combine two rigid bodies into one?

With respect to some fixed frame of reference, given the inertial tensors, positions, orientations, and angular and linear velocities of two rigid bodies, how do you combine them to make a single ...
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2answers
345 views

Interference of EM Waves with Orbital Angular Momentum

If you have two coherent collinear e-m beams of same frequency and polarization, but 180 degrees out of phase, they will destructively interfere. If you introduce orbital angular momentum of L=3 ...
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735 views

Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
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2answers
197 views

Thrust center in space

I have this dilemma: Suppose you have a space ship somewhere in deep space, where there is no drag force or substantial gravity. If the ship has a single engine situated in such a way that the center ...
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1answer
254 views

Clarifications about Poisson brackets and Levi-Civita symbol

I need some clarifications about Poisson brackets. I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
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67 views

What makes a wrist-energized gyroscope rotate faster?

I'm considering a wrist-energized gyroscope, shown below (after my daughter let it fall and it broke open). That one was sold as Roller Ball, but variants are known as Powerball, DynaBee, Dynaball, ...
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64 views

On an Uncertainty Relation for Angular Variables

I'm looking for a proof of the Angular Momentum - Angle uncertainty relation $$\frac{\Delta L \Delta \theta}{1-(3/\pi^2)\Delta \theta^2} \geq \frac{\hbar}{2}$$ which does not involve solving the ...
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2answers
169 views

Solve the angular part of Schrodinger equation numerically

I would like to solve the angular part (the one for what is usually called the $\theta$ angle) of a time-independent 3D Schrodinger equation $$ \frac{\mathrm{d}}{\mathrm{d}x}\left[ (1-x^2) ...
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2answers
201 views

For mesons, or baryons, do sea quarks contribute to the angular momentum of the bound state?

The total angular momentum of a bound state of quarks, such as a meson say, can be done by studying the spin and orbital angular momentum of the 2 valence quarks. What about the sea quarks why they ...
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3answers
1k views

Could life survive a pole shift caused by an asteroid collision?

Could life on earth survive a large pole shift caused by an asteroid collision? I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
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4answers
782 views

Angular momentum power plant on Earth

If tidal power plants are slowing down Earth's rotation then is it theoretically possible to build a power plant that would drain energy from Earth's angular momentum (thus slowing down it's ...
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542 views

What makes the Earth keep spinning?

I am thinking of what makes the Earth keep spinning? Is there anybody here know the answer?
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2answers
936 views

Dynamics of moment of inertia

I'd like to be able to determine the angular acceleration of a system of two rotating masses, which are connected so as to have a variable mechanical advantage between the two. My background with ...
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1answer
155 views

Two components of angular momentum conserved $\Rightarrow $ All three components are conserved?

I was wondering whether it is correct to say that if two components of the angular momentum are conserved, then all three Cartesian coordinates of the angular momentum are conserved? I would regard ...
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278 views

Spinning spheres colliding

In an ideal environment with no friction, in a vacuum, what happens to the velocity of the spin of two spheres spinning in perfect parity at two different velocities when they come into contact?
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578 views

How is angular momentum measured in experiments/in practice? [duplicate]

Possible Duplicate: How does one experimentally determine chirality, helicity and spin? How do you find spin of a particle from experimental data? We read about and study angular momentum ...
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135 views

Commutator not transitive

I noticed the following: $$[L_{+},L^2]=0,\qquad [L_{+},L_3]\neq 0,\qquad [L^2,L_3]=0.$$ This would suggest, that $L^2,L_+$ have a common system of eigenfunctions, and so do $L^2,L_3$, but $L_+,L_3$ ...
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352 views

Quantum mechanical angular momentum and spin formalism/notation

I am currently stuck on the following notation: $\frac{1}{2}\otimes\frac{1}{2} = 0 \text{ (antisym) } \oplus 1 \text{ (sym) }$ No matter what I tried, I couldn't derive the identity. I am sure that ...
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3k views

What determines the direction of precession of a gyroscope?

I understand how torque mathematically causes a change to the direction of angular momentum, thus precessing the gyroscope. However, the direction, either clockwise or counterclockwise, of this ...
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155 views

Angular momentum depends on origin?

The angular momentum of a particle rotating about a point is given by $\vec{L} = \vec{r} \times \vec{p}$. Imagine a particle tracing a circular path on a flat table. If I put the origin of my ...
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337 views

Why can't I just think the spin as rotating?

I'm going mad about the problem. I really don't understand why do electron have 1/2 spin number, why they are not actually spinning. I can accept that the electrons have their own magnetic field, ...
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290 views

What causes matter to initially rotate/spin/orbit?

What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar ...
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4answers
267 views

If angular momentum corresponds to linear momentum, what corresponds to energy?

Angular momentum is defined from linear momentum via $\vec L = \vec r\times\vec p$, and is conserved in a closed system. Since energy is the time part of the linear four-momentum, is there a quantity ...
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1answer
750 views

Can a linear momentum generate angular momentum at collision?

I'm trying to get the facts straight here. Suppose I'm throwing a ball with no angular momentum. It collides with the ground and Newton's third law tells us that a force opposite to the gravity will ...
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2answers
473 views

Quantization of orbital angular momentum

Probably a very simple question, but I can't find the answer on the Internet. I know nearly to nothing about quantum mechanics, but in statistical physics I'm confronted with the idea that the orbital ...
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3answers
121 views

Trilinear gauge couplings: Spin

In non-abelian gauge theories self interaction of gauge fields is permitted, allowing coupling such as $WWZ$ (i.e. $Z$-boson decaying to $W^+W^-$) or ggg (i.e. gluon splitting into two new gluons). ...
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325 views

Angular Momentum Addition Theorem - Sanity Check

Looking back at my quantum mechanics notes, the angular momentum addition theorem is listed as: $j=j_1+j_2,j_1+j_2-1, ..., |j_1-j_2| $ (Using conventional notation) , but I'm a little unsure how to ...
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152 views

Why have $n$, $\ell$, $m_\ell$, $m_s$ been picked as quantum number symbols *in this order*?

I’m learning about electron configurations and don’t quite understand why $n$, $\ell$, $m_\ell$, $m_s$ have been picked as symbols for the quantum numbers. As far as I understand it, the principal ...
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124 views

Matrix representation angular momentum

We are supposed to give a matrix representation of $L\cdot S$ for an electron with $l=1$ and $s=\frac{1}{2}$. I read $L\cdot S$ as $L \otimes S$. Is this correct? Then we would have e.g. for ...
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150 views

Why does $\ell=0$ correspond to spherically symmetric solutions for the spherical harmonics?

In quantum mechanics why do states with $\ell=0$ in the Hydrogen atom correspond to spherically symmetric spherical harmonics?
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Paradox of angular velocity

For a torque-free symmetric top, the Inertia tensor has an inverse $I^{-1}$, and $L=I\omega$. Which implies that $\omega=I^{-1}L$. But since $I, L$ are constants, $\vec\omega$ is a constant. However, ...
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87 views

Why doesn't this equation for orbital motion change with position in the orbit?

The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ...
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2answers
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What does it really mean that particle has a spin of up/down? And how is spin actually meassured?

I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values ...
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1answer
887 views

General procedure for Clebsch-Gordan expansions

I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps ...
3
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4answers
328 views

N particles, will there be any rotation after a period of time or everything will collapse

This is in context of classical Newtonian physics. Consider a system of n different point mass particles. Initially all are spread around on one plane. No particle possess any velocity to begin with. ...
3
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1answer
86 views

A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
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3answers
82 views

Rotational invariance and operator-squares

My mind is drawing a blank right now. In systems with spin and orbital angular momentum, I know that rotational invariance implies that $[H, \mathbf{J}]=0$ where $\mathbf J=\mathbf L+\mathbf S$. But ...
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1answer
976 views

Example where angular momentum and angular velocity are not parallel

I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.
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2answers
453 views

Space Quantization of Quantum Angular Momentum

I am trying to understand what my book is trying to convey. Quantum angular momentum is $L_z = m_l \hbar$ "Choosing arbitrarily a z axis and using an appropriate experimental technique, we measure ...
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1answer
142 views

Mathematically, how do we deduce that angular momentum is bounded?

So, how do we know $J_{+}|j,(m=j)\rangle =|0\rangle$? I.e. that m is bounded by j. We know that $J_{+}|j,(m=j)\rangle =C|j, j+1\rangle$, but how do I know that gives zero? Is it by looking at its ...
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Why is there a phase factor when the two composite angular momentum is exchanged in Clebsch–Gordan coefficients

An identity exists for CG coefficients: $$\langle j_1 m_1 j_2 m_2 |J M \rangle = (-1)^{j_1+j_2-J} \langle j_2 m_2 j_1 m_1|J M\rangle,$$ But why is there a phase factor $(-1)^{j_1+j_2-J}$? It seems ...
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36 views

What determines a progenitor's fate as a spiral or elliptical?

I was thinking about my answer to Are the inner planets on planar orbits because there was more dust in the inner solar system (early on in planetary accretion)? - when it occurred to me that maybe I ...
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816 views

Which force makes a wheel roll down the hill? What causes friction?

A wheel rolling down a hill has two axis of rotation. One is where the center or mass is and the other is the point of contact with the surface which acts as a fulcrum. I was trying to understand ...