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1500 questions
39
votes
2 answers
The formal solution of the time-dependent Schrödinger equation
Consider the time-dependent Schrödinger equation (or some equation in Schrödinger form) written down as
$$
\tag 1 i\hbar \partial_{t} \Psi ~=~ \hat{H} \Psi .
$$
Usually, one likes to write that it has a formal solution of the form
$$
\tag 2 \Psi (t)…
Andrew McAddams
- 6,742
38
votes
7 answers
Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$?
In the book "Quantum Mechanics and Path Integrals" Feynman & Hibbs state that
The probability $P(b,a)$ to go from point $x_a$ at the time $t_a$ to the point $x_b$ at the time $t_b$ is the absolute square $P(b,a) = \|K(b,a)\|^2$ of an amplitude…
asmaier
- 10,250
38
votes
2 answers
Motivation for the use of Tsallis entropy
Every now and again I hear something about Tsallis entropy,
$$
S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1}
$$
and I decided to finally get around to investigating it. I haven't got very deep into the literature (I've just…
N. Virgo
- 35,274
38
votes
5 answers
Why does the pet's water bowl overflow?
So when i give the pet fresh water in a stainless steel bowl that i place on a mat according to the attached picture, from $t=0$ the bowl is at rest, the water normally oscillates in the bowl like a pendulum following the action, but after one or…
user721108
- 493
- 2
- 8
38
votes
3 answers
Is it possible to speak about changes in a physical constant which is not dimensionless?
Every so often, one sees on this site* or in the news† or in journal articles‡ a statement of the form "we have measured a change in such-and-such fundamental constant" (or, perhaps more commonly, "we have constrained the rate of change of...").…
Emilio Pisanty
- 137,480
38
votes
9 answers
Does the curvature of spacetime theory assume gravity?
Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are gravitationally attracted are said to roll down…
Dale
- 6,150
38
votes
3 answers
The Role of Active and Passive Diffeomorphism Invariance in GR
I'd like some clarification regarding the roles of active and passive diffeomorphism invariance in GR between these possibly conflicting sources.
Wald writes, after explaining that passive diffeomorphisms are equivalent to changes in…
user23686
38
votes
13 answers
If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?
I have read that water (or any other liquid) cannot be compressed like gases and it is nearly as elastic as solid. So why isn’t the impact of diving into water equivalent to that of diving on hard concrete?
Hitarth Vyas
- 515
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- 4
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38
votes
4 answers
Gravity as a gauge theory
Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory).
Why should "classical" gravity be some (non-trivial or "special" or extended) gauge theory? Should quantum gravity be a gauge…
riemannium
- 6,843
38
votes
3 answers
Reconciling topological insulators and topological order
We make an important distinction between the topological insulators (which are essentially uncorrelated band insulators, "with a twist") and topological order (which covers a variety of exotic properties in certain quantum many-body ground states).…
wsc
- 5,615
38
votes
4 answers
Redshifting of Light and the expansion of the universe
So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to…
QEntanglement
- 3,941
38
votes
6 answers
How can a Kestrel hover in the wind?
Kestrels are birds of prey commonly found in Europe, Asia, Africa, and the North America. They belong to the falcon family but have a unique ability to hover in the air. You can find a whole bunch of videos (See 1,2,3,4, for example) about these…
AlphaLife
- 13,439
38
votes
2 answers
Why isn't the molecule of water linear straight?
When you see models of water you see something like this:
The hydrogens in the water molecule become negatively charged because the oxygen pulls electrons more. So why don't they repel and move to the opposite sides of the oxygen? Or just form on…
Trevor Blythe
- 499
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- 5
38
votes
1 answer
Why can you see virtual images?
In optics it is widely mentioned real images are projectable onto screens whereas virtual ones can only be seen by a person. Isn't that contradictory? I mean in order to see the virtual image it has to be projected onto the retina (ultimately…
wnrph
- 1,297
38
votes
4 answers
What stabilizes neutrons against beta decay in a neutron star?
Free neutrons are known to undergo beta decay with a half-life of slightly above 10 minutes. Binding with other nucleons stabilizes the neutrons in an atomic nucleus, but only if the fraction of protons is high enough (at least a third or so). But…
Slaviks
- 4,493