The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation
1
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1answer
86 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
72 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
65 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
78 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
51 views
Angular momentum (J) conservation implies angular momentum being parallel to angular velocity?
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
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1answer
59 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
40 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?
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1answer
88 views
Can you help me with physics lab calculations?
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 ...
-1
votes
0answers
31 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
41 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
47 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
43 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
vote
2answers
48 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
33 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 ...
-1
votes
1answer
85 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
30 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
72 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
60 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 ...
0
votes
0answers
86 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
233 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
89 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-Gordon basis, so the conversion looks like:
$$
\begin{align}
...
1
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1answer
86 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 ...
0
votes
1answer
134 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
28 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
130 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
34 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 ...
1
vote
2answers
88 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 ...
5
votes
2answers
75 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 ...
3
votes
2answers
140 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 ...
5
votes
2answers
108 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
88 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
130 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.
1
vote
0answers
85 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
38 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
74 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
189 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
73 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
122 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
74 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
votes
2answers
122 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 ...
1
vote
1answer
67 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
102 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
votes
1answer
59 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 ...
1
vote
3answers
110 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, ...
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votes
1answer
120 views
Does a fundamental principle require specific concepts? [closed]
The angular momentum principle is a fundamental principle. So it can explain a large variety of phenomenon. Doesn't it need concepts like center of mass also for explaining phenomenon? Or just the ...
0
votes
2answers
159 views
Conservation of linear momentum magnitude along a trajectory
I was once criticized for "taking angular momentum as momentum going
in a circle". I was loosely trying to state, in classical mechanics,
that in using conservation of momentum, one can switch between ...
0
votes
1answer
71 views
How to theoretically determine the angular momentum of an atom?
To determine if an atom is a boson or a fermion I have to count the fermions that constitute the atom (protons, neutrons and electrons). My question is: How to theoretically (as opposed to ...
2
votes
1answer
106 views
Decay of metastable state: spontaneous vs. stimulated emission.
I have a question about the upper laser level (the metastable level) in a 3-level laser system. I will call the ground level of the 3-level laser system by "g" and the metastable level by "m".
The ...
0
votes
2answers
170 views
Is it possible to deduce the conservation of angular momentum from the conservation of energy?
Is it possible to deduce the law of conservation of angular momentum from the law of conservation of energy? If possible, by what sense the conservation of angular momentum has the status of law, if ...
4
votes
1answer
106 views
Intuitive understanding of the irreps like Wigner-D matrix?
Wikipedia defines Wigner D-matrix as an irreducible representation of groups SU(2) and SO(3). What is a good way to visualize this representation? Is there any physical system which can be kept in ...
