8 votes

Why $\dot{r} \neq v$?

You can easily think of counterexamples for when the rate of change of the magnitude of the position vector is not equal to velocity. e.g. uniform circular motion. The magnitude of the position vector ...
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6 votes
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Why $\dot{r} \neq v$?

The time derivative of $r$ is not $v$, because this does not take into account motion purely in the $\hat \theta$, $\hat \phi$ direction. Imagine circular motion: $$\frac{dr}{dt}= 0$$ yet there is ...
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  • 5,235
3 votes

How can a neutral atom, e.g., a rubidium atom, be accelerated to a high speed?

One accelerates the Rb as an ion beam, using standard ion accelerators. Now the problem is how to get neutrals from the ion beam. This is achieved through either a charge exchange canal with a ...
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  • 6,750
3 votes

Besides of photon, what else can excite electron from valence band to conduction band, then to form exciton?

In principle, any of the processes that lead to exciton relaxation (i.e., finite time of exciton and electron-hole pairs) can also happen in reverse direction and create an exciton. However, most of ...
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1 vote
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Would the Rutherford gold-foil experiment work inside of an alcohol cloud chamber?

It seems that Rutherford himself saw the tracks of alpha particles in a cloud chamber, Cloud formed on ions due to α-Rays (Image: CTR Wilson Roy, Proceedings of the Royal Society A, Volume 85, Plate ...
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1 vote
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Definite energy states for ammonia molecule (Feynman Lecture Volume III Chapter 9.1)

Hes does not mean that $C_1$ and $C_2$ have to be equal, he is defining the bra $\langle \mathrm{II}|$ from the equation $\langle \mathrm{II}|\phi\rangle=\langle 1|\phi\rangle + \langle 2 |\phi \...
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1 vote
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Understanding rovibrational spectrum for molecules

Your first diagram of relative intensity vs wavenumber shows only the $v=0$ to $v=1$ transitions. At the this temperature the population of molecules in the $v=1$ state available to make the $v=1$ to $...
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  • 990
1 vote
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Find the maximum possible energy for a beta-particle decay-chain

Yes. (Some questions are easy to answer :) )
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  • 4,504
1 vote
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What is the second excited state of $H^{-}$?

You are thinking too much into selection rules. Selection rules do not change the energy, existence, or numbering of states. If you can write down a state, it exists, and its energy doesn't depend on ...
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1 vote

Besides of photon, what else can excite electron from valence band to conduction band, then to form exciton?

A very simple answer might be that any particle which carries energy and has a nonzero cross-section for electrons (which I believe is theoretically true for any particle) could possibly collide/...
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1 vote

Confusion of spin-orbit coupling in Hydrogen atom

I believe that spin-orbit coupling is very badly discussed in text books, for precisely the reason that you describe. The spin-orbit Hamiltonian you quote is the sum of two terms, an electron-field ...
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  • 990
1 vote

Confusion of spin-orbit coupling in Hydrogen atom

It is necessary to ensure that all the terms in the Hamiltonian correspond to the same coordinate system, but you will need to examine all reference frames to make sure that your Hamiltonian ...
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  • 472
1 vote

How to interpret the Uncertainty Principle... between measurements?

The electron's interaction with the nucleus is not performing a continuous measurement on the electron (and vice versa). A measurement does correspond to an interaction between the measured system and ...
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1 vote

Spin of electron after absorbing a photon

As you correctly pointed out, a $\textit{bound}$ electron can absorb a photon (let's just focus on the H-atom for simplicity). To be more precise, one should actually say the system of electron and ...
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  • 387
1 vote

Spin of electron after absorbing a photon

The orbital angular momentum can change by unity: $\Delta m=1$ is allowed for electric dipole transistions.
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1 vote
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Intuition for the $\Delta m = 0,\pm 1$ dipole selection rule

The selection rule for $m$ corresponds to the conservation of the $J_z$ component of the angular momentum, where $z$ is the chosen quantization axis. The $\Delta m=0$ possibility occurs when the ...
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1 vote

Is the $2p\rightarrow2s$ transition possible?

I will narrow the scope of the question as follows: is the transition with spontaneous emission of a photon between the Lamb split levels (i.e. $2S_{1/2}→2P_{1/2}$) forbidden by the dipole selection ...
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