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Jun
15
comment Finding the wave function of a quantum harmonic oscillator
The solution to the Schrodinger equation will give you the wave function, each with a particular energy state. Are you asking "how do I determine what state a particular harmonic oscillator is in?"
Jun
9
accepted Distributional Extension of a Hilbert Space
Jun
9
comment Distributional Extension of a Hilbert Space
I think you have it exactly right - in LQG the Hilbert space is $L_2(\bar{\mathcal{A}},\mu)$ over the space of distributional connections $\bar{\mathcal{A}}$. They must be doing something similar here for the coherent states, but the general language was confusing me. Thanks!
Jun
4
comment How fast would one have to travel in an airplane in order to experience a continuous sunset?
My back-of-the envelope got 975 mph, so I think you've done the right thing. It will certainly depend on the latitude, with higher latitudes requiring lower speeds (until you get to the arctic circle, where you can stay stationary and see the Sun all day). Also, notice that you aren't actually flying around the equator - you want to fly around the elliptic or the Sun would move side to side).
Jun
4
comment Distributional Extension of a Hilbert Space
@ACuriousMind: Ok, I think I see. The deltas are part of the dual space to some subspace of the Hilbert space, equiped with their own measure so that $\delta^*(f)=<\delta,f>$ (or some correct notation!). So the distributions are not expected to be square-integrable, but if you're tricky you might be able to construct square-integrable functions which include deltas.
Jun
4
asked Distributional Extension of a Hilbert Space
Jun
4
revised Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?
added 260 characters in body
Jun
4
answered Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?
Jun
3
comment What counts as information?
@CuriousOne: Wait a second, there's no language problem here - the particles could absolutely be "the experimenters", but it wouldn't change anything about what they know (like you say, the physics is objective but the language is not). Particle B knows particle As state without having to communicate with them, because particle B knows their own state. Plus, "a quantum field" only applies to a subset of known interactions anyway (ie not gravity), so that ontology can't be right.
Jun
3
comment A Quantum Mechanics question that no one can answer
Just to be clear, I think your second two questions are right on the money :-)
Jun
3
comment A Quantum Mechanics question that no one can answer
I strongly disagree with your first statement - I think quantum mechanics is absolutely a complete theory. Rather then getting all upset about Bell's theorem, I'll just point out that neither the interpretation of quantum mechanics nor it's incompatibility with GR (partially solved anyway with QFT) is "part of QM". The first is meta-QM, and the second is explicitly outside of the theory, since it's not supposed to apply at large scales anyway. These are problems in physics at large, not QM.
May
25
awarded  Nice Question
May
21
comment Manifolds, unit 2-sphere and stereographic projection
BTW you can choose more than 2 if you like. Say you break the range of $\theta$ $[0,\pi]$ into 10 intervals $[0,\pi/5),(\pi/10,3\pi/10)...(4\pi/5,\pi]$ (notice these sets overlap - you need that for technical reasons. They can't "just touch"). Then you would have 10 strips, each with values of $\phi$ that run 0 to $2\pi$. Each point is in at least one, and they cover $\mathbb{S}^2$.
May
21
comment Manifolds, unit 2-sphere and stereographic projection
I hope my edit(s) cleared it up. You remove one point (say, $\theta=0$) from one coordinate chart, and you remove the other ($\theta=\pi$) from the second coordinate chart. Now you have two charts which are everywhere invertible and every point ${(\theta,\phi)}$ of the sphere is included in at least one of them.
May
21
revised Manifolds, unit 2-sphere and stereographic projection
I was mislead by the way the question was asked, but it should be more clear now.
May
21
answered Manifolds, unit 2-sphere and stereographic projection
May
21
comment Can't derive FRW Christoffel symbol
Just a minor comment, because I see it a lot. $g^{\sigma\rho}=1/g_{\sigma\rho}$ is easy to write, but depending on what index notation you are using (component or abstract), it may be nonsense. If you mean that "each component of this particular tensor is 1 / ( the component of this other particular tensor )", then I'm fine, but that's only true for the metric if the metric is diagonal. The real relation is $g^{\sigma\rho}g_{\sigma\rho}=1$, true in both abstract and component notation.
May
19
answered Do holes have physical existence?
May
19
answered Is the time “direction” in General Relativity equivalent to a spatial volume
Apr
29
awarded  Taxonomist