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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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 ...
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2answers
309 views

Clebsch-Gordan Identity

I'm trying to take advantage of a particular identity for the sum of the product of three Clebsch-Gordan coefficients, however, the present form of my equation is slightly different. Is there a ...
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46 views

Spin $\frac{3}{2}$ representation in Georgi's book?

Georgi's book Lie Algebras in Particle Physics 2ed equation 3.32 lists the spin operators in the spin $\frac{3}{2}$ representation as: $$J_1=\left( \begin{array}{cccc} 0 & \sqrt{\frac{3}{2}} ...
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1answer
82 views

Does Birkhoff's theorem apply to rotating collapsing stars?

Birkhoff's theorem states that every spherically symmetric vacuum solution to $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time ...
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131 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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101 views

How is $J^{PC}$ value experimentally determined for new types of particles?

How is $J^{PC}$ value experimentally determined for new types of particles? For example, this paper says ... Angular correlations in B+→X(3872)K+ decays, with X(3872)→ρ0J/ψ, ρ0→π+π− and J/ψ→μ+μ−, ...
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2answers
943 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 ...
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2answers
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Angular momentum in a rod rotating around one end?

Sorry if I can't get straight to the point, I have to give a lot of details before I actually state the question. The formula for angular momentum is $L=I \omega$. If we look up $I$ for a thin rod ...
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442 views

Does total angular momentum of the Earth-Moon system include individual rotational angular momenta?

To calculate the angular momentum of a body we need to specify a point (or an axis?) from which to define the displacement vector $\vec{r}$, so that $\vec{L} = \vec{r} \times \vec{p}$. For a rigid ...
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1answer
134 views

Using angular momentum in complex coordinates

So given the angular momentum operator: $$L_{z} = - ih\biggl(x \frac{\mathrm{d}}{\mathrm{d}y} - y \frac{\mathrm{d}}{\mathrm{d}x}\biggr)$$ I know how to write these in terms of polar coordinates ...
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458 views

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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105 views

Total angular momentum of earth

I have problem understanding total angular momentum of earth about center of sun. Consider that earth has an orbital angular velocity of $\omega_0 \hat z$ and a spin angular velocity of $\omega_s \hat ...
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3answers
157 views

How can I find the angular and linear velocity of a 2D body that breaks into two bodies?

Afternoon. This is my first question, so do let me know if I'm doing anything wrong. Looking for help on building a 2D physics game engine with bodies that split in half: I have a two dimensional ...
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1answer
143 views

How to interpret spin observables constructed by non-standard phase choices?

If we try to find matrix elements of ladder operators ( $J_{\pm}$) for spin when they act on eigenstates of $J^2$ and $J_z$ ( $\newcommand{ket}[1]{\left|#1\right\rangle} ...
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1answer
69 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
719 views

Clebsch-Gordan Coefficients for two spin-1 particles - Why is there a ∣0⟩∣0⟩ ket?

I have used the rules for addition of angular momenta to work out the Clebsch-Gordan coefficients, which all seem right except for state $\lvert0,0\rangle$: For n = 1 \begin{align} \lvert1,1\rangle ...
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75 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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305 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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844 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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3answers
328 views

What is predicted to happen for electron beams in the Stern-Gerlach experiment?

The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. ...
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4answers
869 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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708 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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Strong Decay and Parity Conservation?

The following decay is possible according to the PDG and according to my notes it is a strong decay: $$\omega(1420) \to \rho^0 + \pi^0$$ The JPC values are: $\omega(1420)$ 1-- $\rho$ ...
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2answers
382 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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122 views

Radial quantum number for infinite circular well

For completeness, I will sketch the solution of a particle in an infinite circular well first and then get to my question. I apologize in advance since the introduction is standard undergraduate ...
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1answer
155 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. ...
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238 views

Weighing head by angular momentum

A popular Phys.S.E question asks how can I measure the weight of my head. One of the answers suggests measuring the moment of inertia. My suggestion was to construct an apparatus that places the ...
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1answer
189 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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2answers
452 views

Right-angle lever paradox in special relativity

I remember to have read somewhere an interesting special relativity "paradox" considering two perpendicular rods $A$ and $B$ of equal proper length $L$ fixed at point $O$. In the "rest" frame equal ...
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324 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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562 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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977 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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45 views

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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Elegant method to show $[L^2,[L^2,\vec{r}\,]\,] = 2\hbar^2\{L^2, \vec{r}\}.$ [duplicate]

Show that $[L^2,[L^2,\vec{r}\,]\,] = 2\hbar^2\{L^2, \vec{r}\},$ where $\vec{r} = x\, {\hat x} + y\, {\hat y} + z\, {\hat z}.$ "Edit: $\{A,B\} = AB + BA$ is the anti-commutator." I am able to solve ...
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Why are generators defined oppositely in Weinberg's vs. Maggiore's QFT books?

I've been confused about the sign conventions used in Weinberg's QFT book for a long time. Here's my question: The generators $J^{\mu\nu}$ are defined in this book as ...
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Frame dragging resulting in an orbital plane?

In astrophysics today we talked about spinning black holes, ring singularities, and frame dragging. Is this also (to some degree) the cause of the milky way being as flat as it is? Does the spin of ...
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What kind of torques cause an object to precess?

In studying precession, my textbook (Taylor's Classical Mechanics) makes the assumption that a top spinning about its symmetric axis, but tipped at an angle $\theta$, will precess nicely so long as ...
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139 views

Protoplanetary disks, angular momentum and prograde orbits

So you've got a protoplanetary disk and you're going to gravitate yourself some planets together. The disk is made up of the usual planetary system stuff, dust and gas and whatnot, orbiting a common ...
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2answers
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Why is the Milky Way flat? [duplicate]

I read recently that the galactic "flatness" of the Milky Way is due to the rotation of the galaxy combined with a vast stretch of time. Yet, I also read where 1) the Milky Way rotates once every 225 ...
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144 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 ...
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Interchange symmetry for states with identical particles

I was reading this web page about interchange symmetry for states with identical particles here: http://quantummechanics.ucsd.edu/ph130a/130_notes/node317.html The article states that the highest ...
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109 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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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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Eigenspaces of angular momentum operator and its square (Casimir operator)

The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$: $$ [\textbf{L}^2, L_i] = 0. $$ However, the $L_i$ do not commute among ...
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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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Confusion regarding rotational motion!

Let us assume I have a rod of some mass m, moment of inertia I, length l and center C. If I apply a force F on C for a duration of time t, it will accelerate forward. If I apply it elsewhere, the ...
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609 views

An electron in $s$ state

If an electron is in $s$ state, for example in 1s state for Hydrogen or 5s state for Silver atom, $\ell=0$. So,its total angular momentum $L$ is also equal to 0. So, what is electron actually doing in ...
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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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2answers
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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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765 views

Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...