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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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 in ...
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2answers
3k views

Relation between total orbital angular momentum and symmetry of the wavefunction

My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
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Where does the electron get its high magnetic moment from?

I have always found the concept of spin a little weird. I had read somewhere that for the charge or size of electrons, their magnetic field is very high. In order to produce such fields, they must be ...
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How does Delta baryon decay conserve angular momentum?

I'm a chemist so bear with me: I understand the Delta baryons $\Delta^{+}$ and $\Delta^{0}$ to be in some sense spin (and isospin) quartet states of the proton and neutron. These can decay straight ...
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Can the spin of a photon change during its “life”?

Or is the spin set in one of two possible states at its moment of creation and does not change for the rest of the duration of its "life"?
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Our choice of basis surely cannot effect possible outcomes of a measurement?

Common sense says that, of course, the outcome of a measurement on a quantum system cannot be affected by what base we choose to represent it in. However, while studying QM text, it seems like they ...
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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?
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Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?

I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part ...
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What maintains quark spin alignments in baryons?

What maintains quark spin alignments in baryons? The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed. ...
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Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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982 views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
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240 views

Complete derivation of generator of rotations

I have been look all across the internet and every book I could find trying to get a full derivation of the generator of rotations and more specifically angular momentum as a generator of rotations. I ...
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291 views

Effect of rotation on turbulence threshold for Reynolds number?

If the significance of the Reynolds number is: Then what is the effect of angular momentum on the transition from laminar to turbulent as in a convective vortex? Waterspouts, in particular, seem ...
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602 views

Simultaneously commuting set

How does one determine the members of an simultaneously commuting set (of operators)? For example, I have read that for orbital angular momentum, the set is {$H,L^2,L_z$}. How does one know that these ...
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How to get rotational speed after disk-disk collision with friction?

Assume two circular disks A and B collide. They have both initial linear momentum and angular momentum. If their surface has no friction, their angular velocity does not change after collision, so I ...
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Elastic collision of rotating bodies

How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics? I'm writing simple physics engine, but now only simulating non-...
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234 views

How can mean value of a quantity $be$ an operator?

In Laundau & Lifshitz Quantum Mechanics. Non-relativistic theory in $\S29$ a problem is given: PROBLEM Average the tensor $n_in_k-\frac13\delta_{ik}$ (where $\mathbf{n}$ is a unit vector along ...
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491 views

How do objects change their axis of rotation?

If I hold a pencil at its end and spin it, throwing it upwards, it will spin about its end, but will soon start spinning around its center. How is this? I would draw the following torque diagram for ...
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636 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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445 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
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782 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 ...
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What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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Why are pulsar's radiation beams collimated?

Every picture of a pulsar a see shows a very collimated radiation beam. What is the mechanism generating such a collimation? Note: I am not talking about "relativistic jets". I am talking about ...
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291 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) \frac{\...
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What is the Landé g factor?

What is the Landé g factor? I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic ...
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122 views

Sum of angular momentum of all electrons in a magnet

Can the sum of angular momentum of all rotating electrons in all the aligned atoms in a permanent magnet have a significant contribution to the macro angular momentum of the magnet? If yes, why does ...
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79 views

Does the Universe spin? [duplicate]

Maybe it's a stupid question, so I will delete it if it will receive too many down votes but.. I was wondering about the Universe, and the fact that We know it's expanding; We don't know if it has ...
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Half integer eigenvalues of orbital angular momentum

Why do we exclude half integer values of the orbital angular momentum? It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear ...
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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 ...
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Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, $\vec{L}...
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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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176 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?
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433 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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Why do rolling disc (coin) move in circular path?

We have a coin that is rolled such that it's tilted at an small angle $ \theta $. Question:: What turns around rolling disc so that it traces circular motion (spiral as it's speed decreses)? ...
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Spin, orbital angular momentum and total angular momentum

If I understand correctly, spin is an intrinsic property of particles, which follows the algebra of angular momentum, but has nothing to do with an "orbital angular momentum" in that the particle is ...
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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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435 views

The uncertainty in angular momentum

It is known that the different spatial components of the angular momentum don't commute with each other. $$ [L_x,L_y] \propto L_z \\ [L_y,L_z] \propto L_x \\ [L_z,L_x] \propto L_y $$ Also it is known ...
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914 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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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 J^...
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977 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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Why are the magnetic moment and the angular moment related?

Why are the magnetic moment and the angular moment related? I've always read everywhere that they are related but found nowhere a satisfactory explanation of the cause
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quantization of angular momentum

What is the most direct way of observation of quantization of angular momentum?
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Does angular momentum of hydrogen atom imply motion of electron around the nucleus?

Does the non-zero orbital angular momentum (or z-component of angular momentum) of a stationary state of hydrogen atom imply motion of electron (or at least the probability density $|\Psi|^2$) around ...
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Is there a relation between spin and the spin group?

In Quantum Mechanics spin appears as one type of angular momentum. Indeed, in Quantum Mechanics one angular momentum on the state space $\mathcal{E}$ is a triplet of observables $\mathbf{J}=(J_1,J_2,...
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Does a spinning mass follow a straight trajectory in empty space? Or is it curved like a golf ball?

Suppose that we can send to identical satellites (like Voyager 1&2) on identical trajectories. But one spins to the right while the other spins to the left. Would they follow the same trajectory?...
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Can a wave possess spin?

Since a matter wave is associated with a particle in quantum mechanics, does the wave spins? I mean, can we visualize the spinning of wave or is it possible that the wave spins?
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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 how ...
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673 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
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Eigenvalue of $L_z$

In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung... Why is this valid? ...
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Is the conservation of angular momentum violated in electron jumps from one orbital to another?

I don't really know any quantum mechanics. But in our class, we were introduced to Bohr's model of the atom with his postulate that the angular momentum of an electron in the $n$-th orbit is $\frac{nh}...