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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1answer
304 views

Rotating black holes and naked singularity

In the book The science of interstellar by Kip thorne can be found the following: There is a maximum spin rate that any black hole can have. If it spins faster than that maximum, its horizon ...
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9answers
3k views

Physical meaning of the angular momentum

Still reading Classical Mechanics by Goldstein, I'm struggling on a very basic notion: angular momentum. I physically understand it as the momentum of an object rotating around something given a ...
7
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3answers
310 views

What is the origin of spin of celestial objects?

In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is asking about the origin of the rotation of celestial bodies. The ...
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2answers
269 views

Ground state of Spherical symmetric potential always have $\ell=0$?

I was given a problem where I have a spherically symmetric potential (the exact form is not relevant to this question, I think - but anyway is it 0 for $r\in[a,b]$ and $\infty$ everywhere else) and I ...
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1answer
57 views

Where did I go wrong in ket vector in quantum mechanics? [closed]

Consider a system of total angular momentum j = 1. The operator jx is given by: What are the possible values when measuring jx? My attempt: The eigenvalues after calculation are -1, 0, 1. Now I ...
2
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1answer
106 views

Why does dot product equal to one? (Pauli spin matrices)

I was reading these lecture notes (NB: PDF): For spin-1/2, the rotation operator $$ R_\alpha^{(s)}(\mathbf n)=\exp\left(-i\frac{\alpha}{2}\vec\sigma\cdot\mathbf{\hat n}\right) $$ can be ...
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3answers
132 views

Angular momentum

The satellites are revolving around a planet in circular orbits by themselves (no external source to maintain their speed). Are we able to make them revolve in elliptical orbits by themselves? Do ...
2
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0answers
60 views

Do coupled angular momentum eigenstates depend on angle between particle positions?

Suppose we have two particles with positions $\vec r_1$ and $\vec r_2$. The corresponding coupled angular momentum eigenstates would be expressed via Clebsch-Gordan coefficients as (according to this ...
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4answers
347 views

Does the angular momentum vector operator $\hat{\vec{J}}$ have no eigenstates?

Angular momentum projection operators $\hat J_z$ and $\hat J_y$ don't commute, as don't the other combinations of different projections. But this means that there's no such state in which the whole ...
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4answers
1k views

Why Does Angular Velocity Increase as Radius Decrease?

Suppose a child were to ask you why a tetherball (picture below) seems to speed up as it wraps around the pole. How would you explain this to them? Certainly you wouldn't say something like, "Angular ...
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3answers
213 views

Help with Conservation of Angular Momentum Question

An ice skater executes a spin about a vertical axis with her feet on a frictionless ice surface. In each hand she holds a small 5kg mass of which are both 1m from the rotation axis and the angular ...
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0answers
148 views

Torque, angular velocity, keeping track of the rotation of a sphere

I'm trying to simulate a rotating sphere due to a torque on a specific point on the sphere. Say the sphere is connected to a string (so variable length) on the bottom, on $(r, \theta, ...
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1answer
109 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
0
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1answer
285 views

Working towards finding Clebsch-Gordan coefficients for a single electron

I'm really confused about a problem involving a single electron which eventually wants me to calculate Clebsch-Gordan coefficients. I think this is probably because, I've only ever seen examples done ...
0
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1answer
66 views

Two-Body problem confusion regarding equations of motion

I'm reading John Taylor's Classical Mechanics text, and I'm a little confused about something in chapter 8, which deals with the two-body problem with central forces. The issue is with the equations ...
8
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3answers
1k views

What do the Pauli matrices mean?

All the introductions I've found to Pauli matrices so far simply state them and then start using them. Accompanying descriptions of their meaning seem frustratingly incomplete; I, at least, can't ...
4
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1answer
137 views

Misuse of $\mathbf J^2$ in classifying Poincare reps

$SO(1,3)$ has an infinite number of representations, classified by the Casimir invariant $p^2$. $SO(3)$ also has an infinite number of representations, classified by the Casimir invariant $\mathbf ...
2
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0answers
118 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
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2answers
136 views

Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar, \qquad ...
3
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2answers
213 views

What is the cause of planetary rotation. Not orbital rotation [closed]

I am a senior in high school, sixteen years old. I think differently than most in my class. Recently, I have been thinking about alternative causes for the rotation of our planets. My current thought ...
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0answers
19 views

Equation of motion for Rabi resonance method

I am reading this article about Rabi and Ramsey resonance measurement, and I have trouble understanding what happens with the magnetic moment $\vec{J}$ when the oscillating magnetic field is added. ...
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2answers
76 views

Does a ball spin more from left to right than it does from right to left?

I swear that in a manual on tennis published by the German Tennis Association (Deutscher Tennis Bund) it stated as fact that all things being equal a ball will move more from left to right than from ...
4
votes
1answer
344 views

Angular momentum in curved spacetime

It is known that the angular momentum components are also a representation of the $SU(2)$ generators. Given a non-trivial spacetime, say a black hole of some kind or AdS space, how can one define the ...
6
votes
1answer
146 views

How much effort would be required to fix the Earth's rotation?

Given that the earth's rotation has been slowing down by very slight amounts over time, forcing us to introduce leap seconds and so forth into our clocks and calendars, I would like to ask if this ...
3
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1answer
75 views

Why does matter gather as discs around massive objects? [duplicate]

Why do discs, like rings of Saturn and the spiral shape of our galaxy form around massive objects, instead of just a (spherical?) cloud of matter?
0
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1answer
41 views

J-coupling constants and nuclei with zero total angular momentum

The Wikipedia page on J-couplings states that Scalar or J-couplings (also called indirect dipole dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect ...
3
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1answer
180 views

How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?

I'm trying to compute the angular momentum $$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$ where ...
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0answers
58 views

Interpretation of angular momentum in semi-classical vector model

My Professor said that when we calculate the total angular momentum of multiparticles, in this case i.e. 2 particles, we can add total angular momentum by thinking this way, if both spins allign they ...
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2answers
158 views

Why does the Earth rotate on its axis?

I know that the earth moves around the sun because of the gravity force, because the spacetime around the sun is curved. But why does the earth rotate on its axis, and which parameters can affect ...
4
votes
2answers
108 views

Can a Storm make the day longer/shorter?

I've read that changes in jet streams can affect the speed that the Earth rotates on its axis, thus making the day longer or shorter?
0
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1answer
135 views

Are the Pauli matrices closed under commutation?

I tried to make a group multiplication table for the Pauli matrices, but I keep getting multiples in front of the elements. What am I doing wrong? I thought the Pauli matrices formed a group that was ...
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0answers
40 views

Could we imagine spin as rotating probability densities (orbitals) in a kind of expanded orbital model?

I know there is no spin in orbital model. And it is always said there is no visualization for the spin. But why not just let the oribtals rotate with 4D quaternions in some 3D dynamic model?
1
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1answer
109 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom. Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
3
votes
2answers
435 views

What is meant by the spin of a particle? [duplicate]

I have been studying that electrons have quantum number called spin quantum number(s), this number can have either +1/2 or -1/2 value. If s=+1/2, the spin is clockwise and if s=-1/2, the spin is anti ...
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1answer
60 views

How is angular momentum conserved when torque is zero?

According to law of conservation of momentum , angular momentum of a particle is conserved when its torque is zero . Please make it easier for me to visualise this condition .
4
votes
1answer
62 views

Why is the specific notation used for term symbols useful?

This has bugged me for a long time. Term symbols describe electronic states of atoms which have well-defined total electronic angular momentum $J$ as well as total spin and orbital angular momenta ...
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1answer
90 views

What is the 'triangle selection rule' in spectroscopy?

This paper states that However, the multiphonon relaxation bridging the $^5\!D_1$ and $^5\!D_0$ levels is a well-known exception because it is formally forbidden by the triangle rule and occurs ...
0
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0answers
56 views

Quadrupole moment of a valence proton

The state of an unpaired nucleon in the nuclear shell model is given by the quantum numbers $l$, $s$, $j$ and $m_j$ resulting from coupling $l$ and $s$ when we add spin-orbit interaction. In chapter 5 ...
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3answers
173 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
1
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1answer
89 views

Precession in the vector model of angular momentum - quantum mechanics?

The vector model of angular momentum in quantum mechanics says that, for example, the angular momentum vector $\mathbf{L}$ precesses about its projection on the $z$ axis, like this: We can add ...
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0answers
111 views

Can we prove Conservation of Angular Momentum without assuming internal forces are central?

The only proof I've seen of Conservation of Angular Momentum assumes that the internal forces of the system act along the line joining particles i and j (i.e. - all internal forces are central.) Can ...
0
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1answer
70 views

Correct approach for calculating excited states of circular quantum dot under effective mass approximation

From Asnani, Mahajan et al, Pramana Journal Of Physics 73 #3 (2009) p574-580 "Effective mass theory of a two-dimensional quantum dot in the presence of magnetic field", which can be seen here: ...
0
votes
1answer
105 views

When two objects roll down an incline, does the velocity increase?

I know the basics of rotational motion but this question just confused everything: The answer to the question is A. But why? My problems: If first, I treated both the disks as two particles, ...
4
votes
2answers
189 views

How does electron spin change instantaneously without violating inertia principle?

The inertia in one of the main properties of matter. That is why all process in macro world do not happen instantaneously. What I do not understand is how we should apply this general idea of inertia ...
4
votes
1answer
109 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
2
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0answers
41 views

What is the relationship between the angular speed and the diameter of the eye of a water vortex?

In a water vortex formed in a plastic bottle, what is the relationship between the angular speed of the water and the diameter of the hole in the cap? I would have expected that according to the ...
1
vote
1answer
426 views

Definition respective derivation of angular momentum formula

I am reading An Introduction to Mechanics by Kleppner and Kolenkow (2014). On page 241 is the definition of the angular momentum: Here is the formal definition of the angular momentum $\vec{L}$ ...
3
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0answers
56 views

When Did Structures Begin to Orbit in the Universe?

In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
4
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0answers
123 views

Spin via Change of Phase

Thinking of spin as arising from a change in the phase of a wave function: The angular momentum is defined by the change of the phase of the wave function under rotations, which may come from the ...
6
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2answers
786 views

Is there a reason why the spin of particles is integer or half integer instead of even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...