# Tagged Questions

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 does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; ...
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### Do electrons in an atom always have the same 'direction'?

Perhaps speaking of direction of an electron isn't quite correct. But does QM indicates a kind of way whether all electrons are going e.g. 'clockwise' or not? Of course QM just gives a probability ...
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### How can a bowling ball curve in both directions?

There is a popular video on facebook that I just don't understand. A man spins a bowling ball very fast then slightly taps it down the lane. Somehow it does half of a figure eight, curving around two ...
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### Calculating Rolling friction of a car's wheels (NOT ON AN INCLINE)

I'm dealing with a small toy car consisting of a bottle that has a small hole in the back, covered by a thumb tack. The bottle is filled with pressurized air then the thumb tack is released, releasing ...
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### Restriction to the total angular momentum of two identical particles with spin 1

I've been asked if there is any aditional restriction to obtain the possible values of the total angular momentum J by considering that the 2 particles of spin S=1 are identical. If they are not ...
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### Orbital angular momentum eigenstates in the $|\mathbf{r}\rangle$ representation

Consider the orbital angular momentum operators $L^2$ and $L_z$. In the $|\mathbf{r}\rangle$ representation using spherical coordinates those operators actions are given by ...
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### In kerr's black hole solution can the Bekenstein-Hawking entropy be descrete?

In kerr's solution we have: $S_{BH}=\frac{k_{\beta}c^{3}A}{4G\hbar}$ where A is the area of the horizon and equal to $A=8\pi G^2 m(m+\sqrt{m^2 - a^2})$ where $a=\frac{J}{mc}$ and J is the angular ...
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### Generators of cubic group: Euler angles

I am trying to build numerically all members of the cubic group in the representation of Wigner D matrices. Angular-momentum quantum number may be small, e.g. 2, so I use the formula stated e.g. at ...
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### Adding cinnamon to my coffee makes it stop whirling much faster: Why is thats?

When I stir my coffee in a cup, the fluid spins a long time, but when I pour cinnamon into the cup, the spinning fluid slows and stops very rapidly - why?
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### Measuring Rotation of Sun

If the sun had a uniform surface (i.e., if there were no sunspots to look at), is there a practical way to measure its rotation? In other words, if some external force flipped the sun's spin ...
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### How to show the finite rotation of a spin-1/2 system?

I'm reviewing my quantum mechanics by going through Sakurai and Napolitano again and working out all of the derivations. I'm stumped (though I probably shouldn't be) on some algebra in the finite ...
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### What is relationship between linear and angular momentum?

I'm confused about imparting momentum to a sphere, which causes it to rotate without slipping. Does the momentum applied go: only to the rotational motion and the linear is a consequence of the ...
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### How has the world remained in balance?

In the center of our galaxy, there is a Supermassive black hole. We were told in early astronomy units of school that black holes are giant vacuums that will absorb/consume the area around it. My ...