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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2
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2answers
199 views

Peskin and Schroeder Equation 3.23

I've been trying (for a while) to prove that $S^{\mu\nu}:=\frac{i}{4}\left[\gamma^\mu,\,\gamma^\nu\right]$ is a representation of the Lorentz Lie algebra, that is, to prove that it satisfies the ...
1
vote
3answers
220 views

Effect of incoming force on linear vs. angular velocity

First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or ...
5
votes
2answers
865 views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum.But, I was wondering why he quantised angular momentum and any other quantity?
0
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2answers
164 views

Not so simple problem using momentum, energy and angular velocity…?

I have an object in free space (no gravity) with angular momentum $ = \omega_i $, and some velocity vector $=\vec{V_i}$. To simplify we will say it has a mass-less rigid rod length $ = \ell $, ...
4
votes
3answers
264 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 ...
1
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1answer
160 views

Why does $[xp_{y},x]$ commute?

I'm looking at a solution in my book that says $[xp_{y},x]$ commutes. Does bracket notation imply: $[A,B]=AB-BA$ so that $[xp_{y},x]=xp_{y}x-xxp_{y}$ Taking the comment from Max Graves and ...
1
vote
1answer
156 views

Matrix operations on Quantum States in a composite quantum system

Intro (you may skip this if you're an expert, I'm including this for completeness): Say I have two bases for two systems, The first is a spin-1/2 system $|+\rangle = \left(\begin{array}{c} 1\\0 ...
1
vote
0answers
145 views

Is total angular momentum conserved in particle interaction?

Imagine that two electrons interact by exchanging a virtual photon. I know that the total energy and linear momentum of the two electrons is conserved by the interaction. Is the total (orbital) ...
0
votes
2answers
108 views

Angular momentum representation

It is well know that, using position representation $$\langle r\lvert L\rvert \psi\rangle =r \times (-i\hbar\nabla\langle r|\psi\rangle )=r \times (-i\hbar\nabla\psi(r)).$$ However, I read ...
0
votes
1answer
139 views

Does angular momentum conservation imply that angular momentum $J$ is parallel to angular velocity $\omega$?

In other words, does $\frac{dJ}{dt} =0$ imply $J \times \omega =0$? Counterexamples or proofs would be helpful! EDIT: This question originally asked if $\frac{dJ}{dt} =0 \Leftrightarrow J \times ...
1
vote
1answer
219 views

Question regarding mass hanging from center edge of rotating disc

So, say you have a free to rotate disc, assuming no external torques, and you have a spool, radius 7.93 mm, attached to its centre. Say the spool has a string attached to a point on its edge and ...
0
votes
1answer
146 views

Why does the fluid inside a cup not spin when the cup is spinning, but starts to spin when the cup stops spinning?

How come when I spin a cup with water in it, the water does not spin, but the moment I stop spinning the cup, the water starts spinning the other way?
-1
votes
1answer
187 views

Can you help me with physics lab calculations? [closed]

My question is, how do you find the torque of a rotating spool with a connected string being pulled down by its hanging mass? So in this experiment we had a machine with two rotating discs, one on ...
0
votes
0answers
50 views

Can a single atom have angular momentum? At what angel does a single atom reflect a single photon?

Groups of atoms, say two of them, can have angular momentum as a group, but only because they individually have linear momentum and are bound together through a force that causes them to pull on each ...
1
vote
1answer
136 views

Angular Momentum of Two Non-interacting Particles

I'm reading a book (An Introduction to Mechanics by Kleppner) where they calculate the angular momentum $l$ of a system of two non-interacting particles, but I don't understant what are they doing. ...
0
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0answers
70 views

Angular Momentum with Upper Index

I am asked to show $[L^2,L_i] = 0 $, but with the definition : $L^2 \equiv L_i L^i$ I tried this: $[L_i L^i,L_i] = L_i [L^i,L_i] + [L_i,L_i]L^i$ We know that : $[L_i,L_i]$ = 0 , so we have, $[L_i ...
0
votes
0answers
93 views

Photons angular momentum / spin

I have a textbook that says that photons have a spin of absolute value $\hbar$ and at some other point, they say that it has angular momentum of absolute value $\hbar$. Now, since they are different ...
1
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2answers
56 views

Unitary Confirmation

I am asked to show that an new defined operator: $$U_{\beta} = \exp(\displaystyle\frac{i\beta L_z}{\hbar})$$ is unitary, where $$L_z = -i\hbar\,\,(x\displaystyle\frac{\partial}{\partial y} - y ...
-2
votes
1answer
55 views

Can we define angular momentum for the wheel under motion?

According to the definition of angular momentum: Angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and ...
0
votes
1answer
1k views

Cylinder rolling down slope problem [closed]

A uniform cylinder of mass $m$ and radius $r$ is rolling down a slope of inclination $\theta$. The cylinder rolls without slipping. You may take the acceleration due to gravity to be $g$. At what rate ...
0
votes
0answers
58 views

Rotation matrix for a coupled spin system

For an angular momentum basis with magnitude $F$ and magnetic numbers $m_F\in [-F,F]$, the unitary matrix that will perform the Euler rotations is the Wigner-D matrix of order $F$. I have applied the ...
2
votes
2answers
161 views

How does the curve ball drag air around it?

In cricket or baseball there is a type of ball called the curve ball. This is the top spin of the ball.I read that due to spin the ball drags the air around it due to friction in the way shown ...
2
votes
2answers
123 views

Angular momentum matrices (Schiff section 27)

On page 203 3rd edition of Schiff we are given the angular momentum matrices ${J}$ for $j=1$. I am curious as to how these relate to orbital angular momentum for $j = 1$. If we take the corresponding ...
1
vote
2answers
374 views

What is the significance of electron spin quantum number?

Somewhere I read that spin quantum number is a particularly interesting theory of quantum mechanics as what it really implies is that particles like electrons do not come back to the initial state of ...
6
votes
2answers
611 views

Conservation of angular momentum experiment

I've learned in that in this experiment: ...the skater will start rotating faster when she brings her arms in and there is no net torque acting on her. But what would happen to her angular momentum ...
1
vote
1answer
128 views

Shouldn't the addition of angular momentum be commutative?

I have angular momenta $S=\frac{1}{2}$ for spin, and $I=\frac{1}{2}$ for nuclear angular momentum, which I want to add using the Clebsch-Gordan basis, so the conversion looks like: $$ \begin{align} ...
2
votes
1answer
407 views

Hamiltonian matrix off diagonal elements?

I'm trying to understand how Hamiltonian matrices are built for optical applications. In the excerpts below, from the book "Optically polarized atoms: understanding light-atom interaction", what I ...
2
votes
5answers
2k views

Why the center of our galaxy doesn't absorb us?

Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it ...
0
votes
1answer
287 views

Canonical momentum Velocity dependent Lagrangian

I have a homework problem wich I think I'm on the verge of solving but need help with some relations: Show that if the potential $U$ in the Lagrangian contains velocity-dependent terms, the ...
0
votes
0answers
40 views

Russell-Saunders Term

The Russell-Saunders term states that: $$^{2S+1}L_{J}$$ Now, if I'm not mistaken, $L$ is the total orbital angular momentum, $J = L + S$, but what is $S$ exactly? I know it's the total spin angular ...
1
vote
0answers
202 views

Wave functions for 2D potential with spin interactions

So consider a 2D system with a circular potential and a spin-orbit interaction: $V(r) = V_0 \theta(r_0 - r) + c r_0 V_0 L_z S_z \delta(r-r_0)$ where $\theta$ is step function. So the operators ...
2
votes
0answers
67 views

Spin of a decay product

A particle A decays into particles B, C and D. The spin of A, B and C particles is 1/2 each. What are the possible spins of particle D? My attempt is the following: Since B and C have spin 1/2 ...
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2answers
221 views

Can a particle with non-zero angular momentum pass through the center of a spherical potential?

Suppose you have a particle of mass $m$ moving in a potential $V(r) = -\frac{k}{r^2}$, with $r^2 = x^2+y^2+z^2$ and $k > 0$. Since the angular momentum $l$ is conserved, the particle will move in a ...
6
votes
2answers
105 views

How Galaxy is formed?

Given the distance among stars (the most massive objective in the space) is so huge, the difference of order of magnitude is about 7. And also, since gravity is such a weak force, how is it likely for ...
4
votes
2answers
1k 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 ...
9
votes
2answers
714 views

Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
0
votes
1answer
235 views

Conservation of angular momentum

We were learning about angular momentum in class today, and although it sort of makes sense, it's much harder for me to think about than linear momentum. So from what I can tell: Angular momentum ...
3
votes
1answer
1k 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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0answers
200 views

Angular Momentum Conservation in Gravitational Interaction

thanks for any help. I'm trying to show that in a 2body problem, angular momentum is conserved given that $\dfrac{dp}{dt}=\dfrac{-GMm(rv)}{r³}$, where p is momentum, t time, G gravitational constant, ...
0
votes
1answer
240 views

Angular Momentum Conservation in Gravitational Interaction [duplicate]

thanks for any help. I'm trying to show that in a 2body problem, angular momentum is conserved given that $\dfrac{dp}{dt}=\dfrac{-GMm(rv)}{r³}$, where p is momentum, t time, G gravitational constant, ...
1
vote
1answer
86 views

Commutation of abstract $O(3)$ generators and vectors

I've been given the following problem, and I'm quite lost with it. Let $L_1$, $L_2$, and $L_3$ denote the abstract o(3) algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = (B_1, ...
3
votes
2answers
493 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, ...
5
votes
1answer
111 views

Visualizing irreps of SU(N)

What physical system can one use as an example while considering irreps of SU(N)? What is the correspondence between the system and the irreps?
0
votes
1answer
1k views

Nuclear reactions conservation laws

I'd want to know the basic rules to apply the conservation laws in nuclear reactions (nuclear fusion, nuclear fission, radioactive decays, etc.) to determine parity and angular momentum of the ...
2
votes
1answer
157 views

Term symbol - how do we know the number of electrons $e^-$?

Lets say I have a term symbol $^4D_{5/2}$. From this I can simply read the total quantum numbers numbers $L=2$ and $J=5/2$. Now the superscripted number $4$ is called multiplicity if I am not ...
0
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2answers
194 views

LS Coupling - weird image in the book

In the book by Arthur Beiser, Concepts of modern physics, in the chapter LS coupling there is this image: QUESTION: How do we get total orbital angular momentum $L=3$ (image (a)) out of quantum ...
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1answer
405 views

Total angular momentum - single electron

I have been dealing with total angular momentum of the single electron which is outside the closed shells in which sum of the angular momentums is zero. My book says that total atomic angular ...
3
votes
1answer
2k views

What is the scientific reason for the inclination of earth's rotation axis?

This titled position of the earths axis is known as inclination of the earths axis. The earth's rotation axis makes an angle of about 66.5 degrees with the plane of its orbit around the sun, or about ...
0
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1answer
135 views

Motion in a central field and angular momentum

Is it correct that for a motion in a central force field, e.g. a gravitational field, the absolute value of the total angular momentum of the particle and the component of the perpendicular to the ...
2
votes
3answers
186 views

What is the interpretation of the Chern-Simons electromagnetic spin density?

Hans de Vries (who happens to be a no-longer-active physics.SE user) has an online book (referenced below) in which ch. 6 is a presentation of an object he calls the Chern-Simons current, ...