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Silly Goose
Silly Goose
12:34 AM
anyone read Ravi Vakil's notes on algebraic geometry?
 
4 hours later…
naturallyInconsistent
naturallyInconsistent
5:03 AM
@Claudio yes, that is standard from Fuch's theorem
Slereah
Slereah
@ACuriousMind Proposal for names for the various parts of quaternions
The real, imaginary, fantastic and extraordinary
PM 2Ring
PM 2Ring
5:32 AM
@Slereah I'd love to see his names for the components of octonions. ;)
 
2 hours later…
Ryder Rude
Ryder Rude
7:12 AM
String Theory's Leading Contender Suffers Critical Blow
►
This physicist is saying that LQG is almost dead because Lorentz invariance violation hasnt been detected at accessible energies
but this is hypocritical, as string theorists do not take the absence of supersymmetry at accessible energies to disregard string theory
one should be consistent in their criticism
 
5 hours later…
ACuriousMind
ACuriousMind
11:52 AM
@SillyGoose Those are essentially a book, covering what is usually at least a year of algebraic geometry courses. I've not read them fully but what I've read seemed nice, at least as texts on algebraic geometry go :P
 
3 hours later…
imbAF
imbAF
2:38 PM
I have a question about the Zeeman effect. The normal Zeeman effect happens under which conditions ?
 
2 hours later…
imbAF
imbAF
4:35 PM
In the Zeeman effect, whether we are considering the normal or anomalous one, the phenomenon is the result of the interaction of the orbital angular momentum, spin or of the coupling of both with the external magnetic field. But in an atom exposed to an magn. field, when we consider the angula momenta in the calculations, is this the total one of the atom or for individual electrons ?
Silly Goose
Silly Goose
5:31 PM
@ACuriousMind do you know why AG is so "popular"? It seems to be (along with number theory and differential equations) one of the most popular research areas of modern mathematics
I feel like for physics, justifying the popularity of subjects is easier. Quantum gravity is popular because it is like developing a new, "more fundamental" physical theory. Quantum information is popular because of technological consequences. Quantum many-body is popular because of technological consequences. Etc.
Slereah
Slereah
Algebraic geometry is used in cryptography and therefore has large funding from the NSA
Silly Goose
Silly Goose
oh
well that explains it then :P
Slereah
Slereah
user image
ACuriousMind
ACuriousMind
@SillyGoose you're missing several other larger fields, e.g. optimization/control theory, numerics and stochastics, see the arXiv submission numbers
so I disagree with the premise: it's popular, but not "most popular"
imbAF
imbAF
In the stark effect where the disturbance operator is: $$H_1=-eEz$, when considering a spatially/temporally constant electric field that points in the Z direction. The expression above, it seems that is derived by considering an ele. dipole in an electric field. The electric dipole here is because we consider the nucleus and the electron?
imbAF
imbAF
6:03 PM
In multi electron atoms, when we speak about a degenerate spectrum, are we talking about that of the atom or of an electron?
I know that for the H-Atom this distrinction doesn't matter or can be considered as equivalent, But in general
what should one understand when it is said that the atom is in a degenerate state?
Slereah
Slereah
6:15 PM
"Openness and a commitment to research integrity fuels American innovation, but it is not without risk. Malign actors, typically under the direction of a government or corporate entity, can deploy a variety of illicit or illegal methods to draw intellectual capital and advanced technology away from the United States and its partners and allies. An example is the problematic deployment of state-sponsored talent recruitment programs, to exploit, influence, and undermine the research activities and investments of the United States and our allies.
Ah, to be an evil scientist
Silly Goose
Silly Goose
i see
is the electrostatic approximation reasonable for the bohr model of the atom?
naively, I feel like no because thinking about such a model of the atom, it is presumably a very dynamic system
 
2 hours later…
imbAF
imbAF
8:47 PM
How can you predict the splittings of different energy levels (characterized by different values of the quantum number nlm_l) when you consider the angular momentum of the entire atom, which is the same in value for every case ?
 
1 hour later…
Claudio
Claudio
9:50 PM
Once I single out the two behaviors of $u(\rho), \rho = r / a_0, a_0 = \text{Bohr's radius}$, namely : $$ \lim_{\rho \to \infty} \longrightarrow u \propto e^{-\lambda \rho}, \lim_{\rho \to 0} \longrightarrow u \propto \rho^{l+1} $$
If I want to find a solution via power series, would you write $$ u(\rho) = \rho^{l+1}e^{-\lambda \rho}F(\rho), F(\rho) = \sum_{n = 0}^{\infty}c_n \rho^{n}$$ or only $$ \rho^{l+1}F(\rho)$$
I was wondering why would I need to exclude one of the two behaviors for small and large values of $\rho$
This question arises from the fact that Townsend includes both behaviors, while Cohen(and my professor) decide to only include the near-the-origin behavior and don't consider the decaying-exponential-like one very far from the origin
the end result is obviously the same in both cases

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