The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

learn more… | top users | synonyms

0
votes
0answers
13 views

Heisenberg equation of motion for angular momentum operator

I am working on problem 5, from chapter 3 of Sakurai's Modern Quantum Mechanics. The problem has the following Hamiltonian: $$ H = \frac{1}{2}\left ...
1
vote
2answers
42 views

What does “transfer” of angular momentum mean?

The Moon’s gravity produces tidal deformations or “bulges” in the Earth. Because of the Earth’s rotation, the line that goes through the bulges is not aligned with the line between the Earth and the ...
0
votes
2answers
51 views

Transformation of $| JM\rangle$ under the group of rotations

I am following the Quantum Mechanics I, Galindo A., Pascual P. and in page 207 explaining the matrix representations of the Rotation Operators in the angular momentum it appears the next (obvious) ...
1
vote
1answer
69 views

Transforming to a rotating frame in the $x$-basis

I was reading this paper on analytically Solvable driven time-dependent two level quantum systems. The Hamiltonian considered in the paper is the following: $$H=\sigma_z\cdot J(t)/2)+\sigma_x\cdot ...
0
votes
2answers
28 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
0
votes
0answers
22 views

Higher $L$ lower energy?

For multi-electron atoms, what is the physical reason behind the fact that a higher total orbital angular momentum, $L$ gives a smaller total energy, $E$?
3
votes
2answers
69 views

Could 1 force cause a pure moment?

A friend of mine told me if there is only one force, it cannot cause only rotation. I wasn't convinced so I proposed a thought experiment, and now we are both confused. Suppose that we put a rod ( ...
0
votes
0answers
31 views

How to evaluate $[L^2,x_{j}]$ [on hold]

I want to evaluate the following commutator: $[\vec L²,x_{j}]$ where $\vec L= \vec x\times \vec p$, $(L_{i}=\epsilon_{ijk}x_{j}p_{k})$ and $\vec L²=L_{i}L_{i}$, here is my work so far: ...
0
votes
1answer
52 views

Understanding work with rotational momentum/moment of inertia

Apologies for the basic question but between the vectors and the spinning, I'm getting confused. If I have a wheel with moment of inertia $I$ spinning at some rate $\vec\omega$ around an axis, what ...
0
votes
3answers
53 views

Does angular momentum of a system whose Moment of Inertia is changing remains constant?

In this problem, the moment of inertia of system is increasing. Correct option given is (b) and it is argued that no external torque acts. But If moment of inertia is changing , there should be a ...
1
vote
0answers
18 views

Clarification: non-relativistic fine structure of a one-electron atom

The fine structure energy shift (in the non-relativistic limit) for a single-electron atom due to spin-orbit coupling is given by $$\Delta ...
6
votes
1answer
55 views

Tensor product - Addition of angular momenta

In the book Quantum Mechanics - Cohen-Tannoudji, in chapter X, equation (B-5) says $$ \vec{S^2} = (\vec{S_1} + \vec{S_2})^2 = \vec{S_1^2} + \vec{S_2^2} + 2\vec{S_1}\cdot\vec{S_2} $$ and $$ ...
0
votes
0answers
27 views

Rotation operation on spin-1/2 particles

How does rotation operators work on a particle? What does it do on the particle conceptually? Also does particles spin on its axis?
0
votes
0answers
25 views

Eddy current damping heat generation

Background According to this source (page 7): https://deepblue.lib.umich.edu/bitstream/handle/2027.42/109373/me450w10project16_report.pdf?sequence=1 the "braking" torque a magnetic field on a ...
0
votes
1answer
54 views

Quantum Mechanics: Rotation operators

How do I know what direction of the rotation operator to use on the initial state of a spin-1/2 particle? For example, a spin-1/2 particle initially in the $\lvert y \rangle$ state enters a SGz ...
0
votes
2answers
31 views

Momentum of a rack and pinion gear system excited by a time variant force

Background I have a rack and pinion gear system as shown in the image below The pinion gear is attached to a flywheel at the back. The first state of the system, none of the gears or the ...
2
votes
1answer
48 views

Using symmetry to determine a hydrogen electron's decay route from $|300\rangle$ to $|100\rangle$

Lets say we have an electron in state $|nlm\rangle = |300\rangle$ of the hydrogen atom. By selection rules, we know that it can only decay to ground state in 3 ways, namely through the $|21m\rangle$ ...
0
votes
0answers
11 views

Counting the possible states for an electron configuration

How do you find the terms and energy levels for the electron configuration $(n_1p)(n_2 p)(n_3 s)$ in the case of LS coupling, where $n_1, n_2$ and $n_3$ are different? How do you find the number of ...
4
votes
0answers
53 views

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 ...
0
votes
0answers
36 views

Uncertainty in orientation of angular momentum

To calculate the uncertainty it looks like I'm going to find an expression for the root mean square of either $J_x$ or $J_y$, or the $J$ in the x/y plane? But I'm not sure if that's what it means by ...
0
votes
1answer
40 views

Angular momentum definition? [closed]

The definition of linear momentum is this: Momentum is a vector quantity defined as the product of an object's mass, $m$, and its velocity, $\vec v$. So According to that definition,The definition ...
1
vote
0answers
49 views

What is the speed of the skaters in this case? [closed]

You're choreographing your school's annual ice show. You call for eight 60kg skaters to join hands and skate side by side in a line extending 12m. The skater at one end is to stop abruptly, so the ...
3
votes
1answer
26 views

Which force transfers angular momentum in tidal locking?

The moon is in tidal lock with the earth, but a long time ago it was not. As the moon became tidally locked with the earth, its angular momentum changed and the delta went into it's orbit and possibly ...
0
votes
0answers
36 views

Addition of $N$ spin halves

If I have two spin-halves, then \begin{align} \frac{1}{2} \otimes \frac{1}{2} = 0 \oplus 1. \end{align} If I have three spin-halves, then \begin{align} \frac{1}{2} \otimes \frac{1}{2} \otimes ...
0
votes
0answers
45 views

Help finding CG coefficient in Wigner-Eckart Theorem

Here is a Wigner-Eckart problem from class that I am having trouble understanding. $$\langle 310|T_{10}|300\rangle =\langle 31||T_1||30\rangle\langle 10;00|10\rangle $$ where $\langle 10;00 | ...
0
votes
1answer
32 views

Conservation of Angular Momentum for an Object Not Rotating

I have a point mass connected to a string with negligible mass. The point mass has mass $m$ and is moving at a velocity $V$. The string is of length $r$, and it is keeping the point mass tied to a ...
1
vote
2answers
69 views

Angular momentum of rolling sphere [closed]

A sphere of uniform density $\rho$ and radius $r$ is rolling without slipping on a perfectly flat surface. It is moving in a perfectly straight line and its axis of rotation is parallel to the plane ...
4
votes
2answers
64 views

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 ...
1
vote
1answer
23 views

What is the minimal G-force curve in 2-dimensional space?

Given two parallel roads, which need to be connected, what shape of curve would produce the minimum overall horizontal G-force(s) on travelers? Is it a $sin$ or $cos$ wave? Is it a basic cubic ...
0
votes
1answer
35 views

Vector interpretation of Kepler's 2nd law ( r X a = 0 )

I just read the vector interpretation of Kepler's second law and the conclusion put me in a confusion. The interpretation concludes by demonstrating that r X a = 0, where boldfaced r and a are ...
1
vote
1answer
32 views

Isn't there any analog between angular momenta in Classical/Quantum Mechanics, especially for the ground state?

By the ground state, I mean something like the state of the hydrogen atom with the lowest its total energy, where the quantum number $l$ is 0, which means we can't get any orbital angular momentum at ...
1
vote
1answer
55 views

Physical reason behind $\langle +,x | \hat S_z |+,x \rangle=0$? [closed]

For a spin half particle we have the following relation: $$\langle +,x | \hat S_z |+,x \rangle=0$$ I have seen this to derive the Pauli matrices and therefore am wondering without knowing anything ...
0
votes
1answer
34 views

Coriolis object deflection and conservation of angular momenutum

I'm trying to understan kinematic inertial explanation of the apparent deviation of objects due to fictitious forces in rotating Earth. Take an object moving from the equator northwards, or ...
1
vote
1answer
36 views

If a rotating ball gets disintegrated to dust or energy what happens to its angular momentum?

Say a rotating ball or neutron star gets completely annhilated to energy by meeting its anti-matter counterpart (also rotating in the same direction), what happens to the angular momentum? It cannot ...
1
vote
1answer
36 views

Can angular momentum not be conserved in a straight line motion?

Consider a particle moving an a straight line, with constant velocity $v$. The angular momentum (pivot point $O$) can be calculated as $$L=mr v_{\theta}$$Where $v_{\theta}$ is the velocity ...
1
vote
1answer
34 views

Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and no torque is acting?

Why does the kinetic energy of a particle moving in circular motion increase when the turn radius decreases and there is no torque acting? E.g. if a planet is rotating about its axis and it shrinks to ...
0
votes
1answer
61 views

Why does the magnitude of linear momentum of a particle in circular motion change with radius? [duplicate]

My problem is with linear momentum of a particle in circular motion. If we imagine a particle moving around a circle, if there are no torques acting, then we can say its angular momentum is conserved, ...
0
votes
0answers
25 views

Spin Orbital Coupling matrix in p-orbital basis

So I have the following Hamiltonian inherited from atomic Physics: $H_{SOC}=\alpha \vec{L}\cdot \vec{S}=\frac{\alpha}{2}(L^{+}\sigma^{+}+L^{-}\sigma^{-}+ L^{z}\sigma^{z})$ Where L is the angular ...
0
votes
1answer
18 views

Spheres collide with merry-go-round [closed]

Four spheres, with uniform densities $\rho_1, \rho_2, \rho_3, \rho_4$ and radii $r_1, r_2, r_3, r_4$, respectively, roll without slipping with constant velocities $v_1, v_2, v_3, v_4$ along tracks ...
0
votes
1answer
29 views

Angular momentum in rolling about the point of contact

A cylinder of mass 5 kg and radius 10 cm is moving on a horizontal surface with velocity of centre of mass 5 m/s towards right and angular speed 10 rad/s (clockwise) . Find the angular momentum of the ...
1
vote
1answer
41 views

Parallel axis theorem and Koenig theorem for angular momentum

Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics? The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$ Koenig theorem ...
0
votes
0answers
33 views

Relative angular momentum?

Let there be a point $P$. A point $C$ is located at a radius vector $r$ from $P$. $C$ is the centre of mass of a rigid body. The rigid body is rotating with an angular velocity $\omega$ about an axis ...
0
votes
1answer
24 views

Derivative of angular momentum of rigid body

I found this equation that describes the change in angular momentum $\vec{L}$ of a rigid body rotating about a fixed point $O$. $I_o$ is the moment of inertia of the body with respect to the axis of ...
0
votes
1answer
17 views

Calculation of support reaction in rigid body rotation and collisions

I can't understand the logic behind the calculation of torques exerted by supports in rigid body motion, especially rotation. The equation of angular momentum is ...
1
vote
1answer
38 views

Why is the center of mass frame always used in rigid body dynamics?

In most of the cases the center of mass is chosen for rigid body motion description, but this is not an obliged choice, since the motion of any point $P$ of the rigid body can be seen as the ...
0
votes
2answers
38 views

Disk let free to rotate

A rigid body moving with no constraints, in particular rotating, will rotate necessarily about a principal axis of inertia. I thought that the reason of this is that otherwise, the angular momentum ...
0
votes
1answer
38 views

Principal axes of inertia of a compound pendulum

I am confused about principal axes of inertia. Consider the compount pendulum in the picture, made of a rectangular plate. I oscillates about a horizontal axis $\hat{a}$ passing through $A$. The ...
0
votes
0answers
29 views

Spin Orbit Coupling Hamiltonians

I am really struggling with something fundamental. I keep coming across two versions of the hamiltonian for spin orbit coupling: $H_{soc}=\frac{\mu_B}{2c^2}(v \times E) \cdot \sigma $ $\mu_B =$ ...
0
votes
1answer
30 views

The MRI signal: why do we consider the phase in the MRI signal

I am trying to understand the imaging principles behind MRI and I was looking at some lecture slides found here Specifically, I am looking at slide 41 where we look at some of the equations regarding ...
0
votes
1answer
25 views

Deviation of free falling objects (Coriolis effect) using conservation of angular momentum

I read this pdf damtp.cam.ac.uk/user/stcs/courses/dynamics/lecturenotes/section4.pdf on non inertial frame, in particular I have a question on the deviation of free falling object due to Coriolis ...