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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187 views

Angular momentum in planetary disk formation

This question is actually more linked to astronomy and astrophysics than to pure physics. I tried posting it on the astronomy page, however it got no answers, so I though this page might help. ...
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2answers
241 views

Why are the spin operators defined as they are?

$$\begin{align*}S_z &= \frac{\hbar}{2} \left(\left|+\right>\left<+\right| - \left|-\right>\left<-\right|\right)\\ S_y &= i\frac{\hbar}{2} \left(\left|-\right>\left<+\right| - ...
2
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1answer
54 views

For Charmonium, why does the spin-spin interaction mostly affect the $L = 0$ states?

For Charmonium, why does the spin-spin interaction mostly affect the $L = 0$ states? My textbook states that this is because "only then is the wave function at the origin non-vanishing". Could anyone ...
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2answers
1k views

Need help with relationship between angular momentum, linear and angular velocity

I am in an introduction to engineering physics course and just trying to see if my understanding of angular motion is correct or if I have the wrong idea. So as I understand it, angular velocity is ...
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2answers
66 views

How did the planets (in the Solar System) start to revolve around the sun if they were attracted towards the Sun via the gravitational force? [duplicate]

The planets in the Solar System revolve around the Sun in almost circular paths called orbits. The Sun pulls the planets with the gravitational force,but the planets do not get drawn to the Sun but ...
0
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1answer
68 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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1answer
50 views

Pipe in space outputs gas - what is its angular momentum at $t$ and $t+dt$? [closed]

Given a pipe in space (neglect gravitational force): The speed of the gas is $v_0$ (in relative to the edge of the pipe) The length of the pipe is $l$ The pipe rests (not moving) at $t=0$ The gas ...
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1answer
55 views

Calculating values related to angular momentum and then their uncertainties [closed]

Here is the problem: And here is my work (sorry it is handwritten, it would take a while to type this out) My problem is that I'm not sure if it's right or if it makes sense to keep getting 0 ...
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1answer
146 views

Question about angular momentum operator

To show that the eigenvalue to $L^2$ is proportional to $\hbar^2$ is shown from $L_z=xP_y-yP_x$ $p_y=-i\hbar\frac{\partial}{\partial y}$ $p_x=-i\hbar\frac{\partial}{\partial x}$ $L_z=-i\hbar(x\...
0
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1answer
373 views

How does the Earth rotate, given that the torque acting on it while revolving is zero?

I've come to understand that the torque acting on the Earth while revolving the Earth is zero. Torque is the force responsible for rotation of a body. So how does the Earth rotate?
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3answers
2k views

How does frequency change with centripetal force?

Using the equation $$F_c = {{mv^2}\over{r}}$$ I can see that mass and velocity are directly proportional to centripetal force. I can also see that the radius length is inversely proportional to ...
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1answer
81 views
5
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2answers
228 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 ...
2
votes
1answer
68 views

Connection between half and whole integer eigenvalues for orbital angular momentum [duplicate]

I have been trying to follow this derivation from Sakurai and Shankar, pulling from both. I would like to see how the following derivation can be extended to orbital angular momentum, and thus find ...
0
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2answers
589 views

The uncertainty principle and spin

I realize that this may be a very basic question, but I've been unable to find the answer elsewhere so thanks in advance for the help. Suppose an electron's spin is measured about an axis, and then ...
1
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1answer
431 views
7
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2answers
341 views

Will an object falling into Earth's orbit start spinning?

Assume an object falls towards Earth (I've drawn a hyperbolic orbit, but this would apply to any orbit). The object starts at $A$, and at this point it is not rotating i.e. an observer on the object ...
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0answers
36 views

Dynamics inside a rotating spaceship

I have been thinking about this question for a long time and I din't find an explanation in the web for it lets say that we a rotating spaceship in the shape of cylinder, that is rotating in an ...
0
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1answer
222 views

Wigner $d$-matrix for $j=1$ [closed]

In Sakurai's Modern Quantum Mechanics p.198-199, he states that for the matrix $$J_y^{(j=1)} = \frac{J_+-J_-}{2i} = \frac{\hbar}{2} \begin{pmatrix} 0 & -\sqrt{2}i & 0 \\ \sqrt{2}i & 0 &...
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1answer
341 views

Basic question about angular momentum

I've learned that the angular momentum of an object rotating about a fixed axis is $I \omega $. Also, in absence of external torques, $I_1 \omega_1 = I_2 \omega_2 $ (meaning, two different events). I ...
0
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3answers
208 views

QM rotation operator

I have seen the proof that for fermions a rotation of $2 \pi$ does not return a spin angular momentum eigenstate to its original form, but instead multiplies the wavefunction by $-1$. Here is an ...
5
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1answer
232 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 ...
0
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2answers
209 views

How does a wheel balance itself during circular motion? [duplicate]

A wheel (or any ring of considerable mass) hardly balances itself when it is placed vertically on ground, but when we roll it along the ground it balances itself. What causes this effect? I guess its ...
0
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1answer
58 views

Kepler's laws: show the planet always stays in the same plane?

I know angular momentum $L=q \times p$ is conserved, where $p=L_{\dot q}$ is linear momentum. How to apply this to a planet orbiting the star, described by the position vector $q$ relative to the star....
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1answer
98 views

Why dosen't my boomerang return [closed]

My boomerang I built will only turn just a bit back towards me, but that's it, but why? Is it my design, I incorporated the recommended dimensions from the website I used, such as an 107 degree ...
0
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2answers
431 views

How does angular momentum affect the trajectory of a projectile?

I am thinking about a football thrown in a very tight, very fast spinning spiral. If the football is thrown upwards at a high angle, is it possible for the football to not turn over at the top of its ...
0
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2answers
179 views

Why only 1 component of angular momentum?

Griffiths says that you can have only 1 well defined component of the angular momentum because of the uncertainty principle. From the uncertainty principle, we get that $$ \sigma_{L_x}\sigma_{L_y} \...
0
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1answer
370 views

How do you add angular momentum of three or more particles in quantum mechanics?

I'm trying to find some information on how to add the angular momentum of three or more particles, but all the sources I look at deal with only two. In this case I understand that if the angular ...
0
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1answer
48 views

How to get moment from angular momentum

I have a mass spinning while attached to a string as shown in the diagram: I can calculate the angular momentum of the mass as I know it's shape and rate of rotation (in deg/s). I want to calculate ...
3
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2answers
594 views

An identity of Pauli matrices

I am studying spin recently, and textbook gives some identities of Pauli matrices, one said that for any two unit vectors $\bf m$ and $\bf n$, $[\bf m \cdot \bf{\sigma},\bf {n \cdot \sigma}]= 2i(m\...
3
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2answers
174 views

How to associate a Hilbert space with a QM system?

I couldn't really find a fitting title for this question. I'm still relatively new to QM and am trying to get the basics down. I understand that a physical system is associated with a Hilbert Space, ...
0
votes
1answer
82 views

Tensor operators and transformation of $O^s_{\ell}|j,m,\alpha\rangle$

In H. Georgi's Lie Algebras in Particle Physics one defines a tensor operator transforming under the spin-$s$ representation of $SU(2)$ as the set of operators $O^s_{\ell}$ (for $\ell=-s...s$) such ...
2
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1answer
283 views

orbital angular momentum of the silver atom

In a silver atom, the first 46 electrons are all paired and according to David McIntyre in Quantum Mechanics, The electrons in the closed shells can be represented by a spherically symmetric cloud ...
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1answer
221 views

Why do planets not stop revolving around the Sun? [duplicate]

Why do planets revolving around the Sun not stop revolving? Note I am not asking why planets do not collapse with Sun.
2
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0answers
41 views

Simplification of matrix-element given the Wigner-Eckardt theorem and Clebsch-Gordon coefficients of a 1,1/2 system

How can I simplify the following matrix-elements $$\left\langle 1,1/2;m_1,m_2\left| S \right| 1,1/2;m_1^{'},m_2^{'} \right\rangle$$ given the Wigner-Eckard theorem $$\left\langle j,m|S|j^{'},m^{'} \...
0
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1answer
174 views

Why do particles have spins such as $1/2$, $3/2$, $5/2$? [duplicate]

What does it mean to have 'half' spin? I have looked on Wikipedia and a few youtube videos on spin but they don't explain what it means to have $1/2$ spin. I am 18 and only starting to learning about ...
2
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0answers
86 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation $\omega~\text{rad/s}...
2
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1answer
48 views

Azimuthal angle in bloch sphere

I was wondering if there is any direct physical meaning behind the Bloch sphere parametrization in the sense that if I choose the angle $\phi =0$, then what does this mean for my spin state? Does ...
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2answers
226 views

Proving that conservation of momentum doesn't apply to electron in H-atom

To prove that the conservation of linear momentum doesn't apply to electron in H-atom, is it sufficient to show that angular momentum operator ($\hat L$) and momentum operator ($\hat p$) do not ...
2
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1answer
92 views

Question about surface term in QFT problem

I am trying to follow the solution of the following problem (Srednicki 39.2): To show that: $$J_z b_s^\dagger(p\hat z)|0\rangle=\frac{1}{2}\ s\ b_s^\dagger(p\hat z)\ |0\rangle, $$ where $J_z$ ...
0
votes
1answer
107 views

Boomerang angular momentum

So I'm building a boomerang to fly 200 feet in order to do that I was told to increase the moment of inertia to increase the resistance from change in state, and I was told that it would increase the ...
1
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3answers
387 views

How can you conclude that the angular momentum of a particle moving in a central field of force will be constant?

When determining the magnitude of the angular momentum vector $|\vec L |$, for a particle in a central field, my textbook concludes the following: $L=|\vec{r}\times m\vec{v}| = mr^2\dot{\theta}$ = ...
4
votes
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} \newcommand{avg}[1]{\left\...
1
vote
0answers
145 views

Relative velocity between a ball hitting a rod [closed]

A ball of mass $m$ travelling with a velocity $v_0$ collides elastically, and perpendicularly with a rod at a distance $d$ from the center of the rod. The rod has a mass $M$ and lies on a frictionless ...
1
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1answer
428 views

Conservation of angular momentum in a free rod

When a collision is elastic and no external torque acts on a system, angular momentum is conserved I found this example and checked the results: A ball (m = 1 Kg , v = p =+22 m/s, Lm = +11, Ke = 242 ...
2
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2answers
86 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
1
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1answer
69 views

Is the distance involved in calculating angular momentum to an axis or a point?

I'm a high school student.I still don't really understand angular momentum and moment of inertia. I know the moment of inertia of a point mass is defined as $mr^2$. For any other shape, we integrate ...
2
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1answer
46 views

Angular momentum effect on quantum energy

I'm doing some computational research into quarkonium states and I've written a code that determines energy levels by finding a solution to the Schrodinger equation for a given angular momentum. I.e. ...
1
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1answer
499 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
2
votes
2answers
415 views

Dumbbell rotation

What if apply impulse to dumbbell consisting of two masses and massless rod? It is clear for me that left dumbbell will move straight line. But it is not clear for me what kind of motion will have ...