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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32 views

Is angular momentum the conjugate momentum of an angle?

Lagrangian mechanics can be used to describe the double pendulum (see here, for example). In this development are the conjugate momenta $p_{\theta_i}$ exactly the angular momenta $m_i l_i \frac{d ...
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1answer
30 views

About shift operators

The question is this: Does $$L_+ L_- Y_{lm} $$ ,where $Y_{lm}$ is a spherical harmonic function, equals to zero. If so, why? The two operators above are defined as $$L_+ ={L_x + iL_y } $$ $$L_-={L_x ...
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28 views

Angular momentum wavefunctions with respect to different axes

I've been learning about quantum angular momentum, and I have a question about the relationship between quantum mechanical angular momentum wavefunctions with respect to different axes. I know that ...
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0answers
49 views

Angular momentum of light in classical electrodynamis [closed]

I' reading at this time electrodynamics from Griffith's Introduction to electrodynamics. As i see, to have the conservation laws in field theory we have to consider the fields as carrying energy, ...
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0answers
29 views

Determine the speed of balls after collision [on hold]

I am sorry for my English it is not perfect at this moment but I hope you will understand my question. I have a problem with solving this exercise. The two balls of the same density and radius r and ...
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1answer
6 views

What happens to the velocity map image if the plane of polarization is not on the plane of the detector?

In an electron Velocity Map Imaging (in Velocity Map Imaging in general) it is required that the plane of polarization to be parallel to the plane of the detector (in other words, plane or ...
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1answer
98 views

Problem on Einstein - de Haas experiment

I am a Physics student (4th year) and I'm trying to study the Einstein - de Haas effect in laboratory. That is what I got: a suspended Iron cylinder with about 5 cm height and a radius of 0.8 cm is ...
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29 views

Rotation of a spin polarization meaning

I've got some quantum state $|s\rangle =\left( \begin{array}{c} cos(\frac {\theta}{2})\\ {e}^{i\phi}sin(\frac {\theta}{2})\end{array} \right)$ I operate on it with a Paul matrix $\sigma_z$ and get a ...
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1answer
37 views

Why is this spin expectation value a vector

I'm given a spin state: $|s\rangle$ = some linear combination of $|\uparrow\rangle + |\downarrow\rangle$ possibly with an imaginary component. $\hat{\mu}_e = g\mu_B\hat{\sigma}$ $g$ is the ...
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1answer
29 views

How do I find an expectation value for an electron's magnetic moment?

Given a spin state: $|s\rangle$ = some linear combination of $|\uparrow\rangle + |\downarrow\rangle$ possibly with an imaginary component. How do you get from the definition of a magnetic momentum ...
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21 views

Atomic physics, determining levels and terms

In atomic physics I understand there a configurations, terms and levels. I think levels for instance appear because of spin-orbit interactions, so that terms are split. But I'm confused about the ...
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52 views

Why do $S_x$ and $S_y$ flip up/down spin states but $S_z$ does not?

By using the notation $S\lvert s,m_s\rangle$, such that $\bigl\lvert\frac{1}{2},\frac{1}{2}\bigr\rangle=\lvert+\rangle$ and $\bigl\lvert\frac{1}{2},-\frac{1}{2}\bigr\rangle=\lvert-\rangle$ we can ...
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428 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
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1answer
39 views

Spin of a particle (Quantum Mechanics) [duplicate]

Why the intrinsic spin cannot be expressed in terms of polar vectors or the orbital variables $\bf r$ and $\bf p$? Or, why do we need matrix representation for Spin?
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2answers
91 views

How many hours will be in a day if the radius of Earth increases by 70 m?

I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ...
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1answer
56 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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248 views

Azimuthal quantum number $\ell$ and magnetic quantum number $m$ are from angular momentum?

Azimuthal quantum number $\ell$, and magnetic quantum number $m$ are defined when we do derivation for $L^2f=\ell(\ell+1){\hbar}^2f$ and $L_zf=\ell{\hbar}f$. This is my own conclusion after studying ...
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33 views
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2answers
74 views

Will the day/night cycle change when the poles melt?

I want to know what will happen to day and night if poles melt i think it will change but I don't know why? ^_^
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1answer
76 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 ...
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0answers
24 views

How do I find the electron confinement energies in a spherical quantum dot?

So if I've got a spherical quantum dot, we'll say it has a 10nm diameter for simplicity. This dot is a semiconductor and it has an electron with an effective mass altered by a factor of 0.2. How do I ...
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1answer
40 views

Angular momentum-torque relationship in a rotating frame?

I have read that $$\vec\tau=\frac{\mathrm{d}\vec L}{\mathrm{d}t}$$ holds true whenever the origin is not accelerating. But I cannot see why this holds true for a rotating frame of reference (such as ...
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2answers
65 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
85 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
1k views

How is parity relevant to determining angular momentum?

Question: Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B. What are the allowed values of the orbital angular momentum $\mathbf{L}$, ...
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3answers
181 views

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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3answers
49 views

Why is acceleration significant to generating power in racket sports?

I'm reading a paper on badminton stroke power (see Figure 4 on page 8). It says: For most of the trials the racket head reached peak speed just at the time of impact. The racket head showed ...
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2answers
69 views

Clarify an assertion on torques from the Feynman lectures

In The Feynman Lectures, vol.I, chapter 18, Feynman discusses torques on a rigid body in two dimensions and says: Now we pause briefly to note that our foregoing introduction of torque, through ...
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2answers
48 views

Angular momentum commutation relations?

Does any operator $\mathbf{T} = (T_1,T_2,T_3)$ that satisfies the commutation relations $[T_i, T_j] = i\hbar\epsilon_{ijk}T_k$ represent an angular momentum operator?
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1answer
47 views

Do all “normal” black holes rotate?

Can we assume that most (if not all) black holes are rotating, due to conservation of momentum? I am excluding the micro world from this question, just thinking of the range of stars on the main ...
3
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1answer
243 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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82 views

Can gyroscope work in zero gravity?

Most ships have two or more gyroscopes to balance on water, man made satellites uses gyroscope for orientation as they fall around earth. All these applications seems to be associated with gravity, ...
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24 views

How can a rotating cylinder produce lift? [duplicate]

In the air, the velocity and angular momentum that causes a force against gravity is lift. How can a rotating cylinder make lift with angular momentum?
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54 views

Conservation of angular momentum in a planetary system

Why is angular momentum conserved when a planet revolves about sun in an elliptical orbit? Why is linear momentum not conserved in this case? Please use the minimum amount of equations and try to ...
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2answers
84 views

How do I prove that the del squared operator commutes with the angular momentum operator? [closed]

I need to prove in Cartesian coordinates that $[\nabla^{2},\hat{L_{z}}]= 0$ I know that the angular momentum operator is defined as: $\hat{L_{z}}=x\hat{p_{y}}-y\hat{p_{x}}$ And the del squared is ...
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2answers
314 views

Conservation of Angular Momentum and linear velocity

I have a problem where a cylinder is moving on a horizontal surface, starting with velocity $v_0$. It is given that its radius is $10\text{cm}$, its mass is $200\text g$ and the coefficient of ...
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2answers
74 views

Combinations of angular momentum

The following diagram is taken from this Wikipedia page: It illustrates how we may only know the total orbital angular momentum $L$ (so the radius on our sphere in $L$ space) and the z-component of ...
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1answer
91 views

What's the significance of the difference between the quantum numbers, $\ell$ and $m_{\ell}$?

I know that $m_{\ell}$ is associated with the projection of the angular momentum vector onto the $z$ axis and $\ell$ is associated with the length of the angular momentum vector. To me this implies ...
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1answer
70 views

Considering spin angular momentum, what is the magnetic moment of a hydrogen 1s electron, and its energy levels?

This question, posed in a problem sheet that I have been asked to do, has stumped me. I really don't know what to do here. Any help would be greatly appreciated. I know that the magnetic moment of an ...
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1answer
110 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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1answer
35 views

Ignoring spin, what is its orbital magnetic moment of an electron in a hydrogen atom in the 2p orbital?

I know that a magnetic dipole moment is given by $$\mu=\frac e{2m}I$$ and that the angular momentum is $$\frac {m_jh}{2\pi}.$$ However, I have also seen that angular momentum $I$ is given by $$I=\frac ...
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1answer
66 views

Why is orbital angular momentum quantized according to $I=\frac h{2 \pi} \sqrt{l(l+1)}$?

I simply have no idea how this result is found $$I=\frac h{2 \pi} \sqrt{l(l+1)}.$$ The result seems to just be dumped in textbooks rather than explained. I can get the result that ...
2
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3answers
97 views

Discovery of spin-3 particle at LHCb

I just read a discussion on the CERN website regarding first observation of a heavy flavored spin-3 particle at LHCb. This appears to be a post from last July. Is there anyone knowledgeable enough in ...
3
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5answers
4k 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 ...
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1answer
229 views

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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1answer
59 views

Difference between quantum numbers j and m and the four others

I am confused about what is the difference between the quantum numbers $j$ and $m$ and the other four quantum numbers: the principal quantum number $n$, angular momentum $m$, etc.? From Quantum ...
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1answer
62 views

What is the Kerr factor for Sagittarius A*?

I have searched for it, but everything what I found is that A0620-00 (the current closest black-hole to Earth) is a slow spinner with Kerr factor $a=0.12$. How about the Kerr factor for Sagittarius ...
2
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3answers
163 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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1answer
33 views

Time evolution of generalized angular momentum operator

We define this operator : $$M^{\mu\nu} = \int d^3x~(x^{\mu}T^{0\nu} - x^{\nu}T^{0\mu})$$ where $T_{\mu\nu}$ is the energy momentum tensor (see e.g. Energy momentum tensor from Noether's theorem) ...
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2answers
68 views

What should we do If we wanted to increase the angular velocity of a planet? [duplicate]

We could hit it with really fast objects, but could we manipulate the orbit of a large satellite to speed up its rotation? What would be the easiest way?