# Tag Info

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If one of the rules to be a planet is that it needs to clear ALL objects from their orbit, does this also make Neptune a non-planet? This is a somewhat common misconception of the meaning of the term "clearing the neighborhood". None of the planets could be called "planets" if clearing ALL objects from the vicinity of the orbit was what that term meant. ...

8

Neptune actually is the dominant gravitational force in the region of the Kuiper belt in which Pluto resides. In fact, if you look at the image below, the belt is being cleared out by Neptune: In fact, there is a class of objects, suitably named the plutinos, that have been captured by Neptune. Solar system models have actually shown that Neptune was ...

6

The sort of trick involved in removing the $|P\rangle$ on both sides to get the conjugate imaginary equation $$\langle P|\xi|P\rangle = \langle P|a|P\rangle \tag1$$ is quite common but it is indeed nontrivial to grasp the first time. In essence, you leverage the fact that in an equation of the form $$⟨\psi|\hat A|\phi⟩=⟨\psi|\hat B|\phi⟩\tag2 ... 6 The bound state is defined such that the probability density average will be finite at some particular space region when time passes. While for unbounded states, as time passes, the probability density will tends to zero. See Landau Quantum Mechanics section 10. This can be understand as this, if the state is bounded, i.e. it is exist only within some ... 4 We use the term mass, when we mean the mass of a weight, and we use the term weight, when we mean the weight of a mass. :-) The important thing to remember is, that the mass is the same everywhere, while the weight varies with the local gravity. So if you are referring to the constant mass of an object, you use mass expressed in kg. If, however, you mean ... 4 If you want to restrict the question to numerical quantities that have physical units, sometimes they are called "dimensionful quantities" in contrast to "dimensionless quantities" that have no units, see p. 6 of Introduction to Classical Mechanics by David Morin for an example of such usage. 4 "To clear an orbit" has a specific meaning which may not entirely intuitive. "Clearing an orbit" specifically does not mean emptying an orbit of all other bodies. It means the planet gravitationally dominates other bodies at approximately the same distance to the sun. Now you can wonder perhaps whether Neptune dominates Pluto or Pluto dominates Neptune. ... 4 We can't see in the heads of committee members, but to understand the tradition of "what for what" in Nobel prizes, I think it is instructive to see the chain of Nobel prizes awarded for developments connected to nuclear magnetic resonance (NMR). Here's a list. There were three prizes in Physics during 1943-1952, two prizes in Chemistry during 1991-2002 ... 3 Since states which are not eigenstates of the Hamiltonian are also not eigenstates of the time evolution, it does not make sense to talk about "bound states" for these states, as they are continually changing into other states. For energy eigenstates, it makes sense to speak of "a bound state", since that state will stay the same forever unless acted upon. 3 So I've done some further research into this question and the result I found is quite surprising. There truly is no set definition. Some cosmologists will tell you (as John Rennie mentioned) to avoid using the term "Big Bang" unless you absolutely have to. However, that is a luxury not afforded to all cosmologists. The more surprising thing is that among ... 2 Apparently it's a historical quirk. Characterizing spectral lines as principle, sharp, or diffuse dates back to the 1870s with the works of George Liveing and Sir James Dewar. Living and Dewar also noted that these lines appear in series. Arno Bergmann discovered a fourth series in 1907, which he labeled as the fundamental series. If Arnold Somerfeld had ... 2 If you care about the inertia you use "mass". When you are considering the force of gravity you use "weight". So when you do calculations about the force in the cables due to acceleration of an elevator car you need to know both it's mass and it's weight... The (calibrated) object you place on a scale is called a "weight" - because that is the property you ... 2 Hopping and tunneling are often used as synonyms, but they are really very different terms with a fundamentally different basis. Tunneling is an inherently quantum-mechanical feature which means that a particle wave-function tends to overlap into it's energetically disallowed area which leads to a non-zero probability of finding it "where it should not be". ... 2 Bound states are usually understood to be square-integrable energy eigenstates; that is, wavefunctions \psi(x) which satisfy$$ \int_{-\infty}^\infty|\psi(x)|^2\text dx<\infty \quad\text{and}\quad \hat H \psi=E\psi.  This is typically used in comparison to continuum states, which will (formally) obey the eigenvalue equation $\hat H\psi=E\psi$, but ...

2

The concept of inertia is indeed useful in two ways. I think your notion of it as a technical promotion of the everyday word "sloth" (without the baggage given it by the Roman Catholic translation of the "deadly sin" Ἀκηδία) as extremely close to the mark. In physics the notion of "inertia" has two, very alike uses: The first is practical, through a weak ...

1

I think your confusion (like mine) is simply over technical English usage. As you rightly state "vectors look like passive elements on which the group matrices act, and do not contain the structure of the group". To my mind, a representation of a group is a triple $(\mathfrak{G},\,V,\,\rho:\mathfrak{G}\to GL(V))$: the group $\mathfrak{G}$ being ...

1

Now that I have a better understanding of what you're asking, I think a good candidate would be "quantity value", also known as the "value of a quantity", from p. 28 of the International Vocabulary of Metrology, Basic and General Concepts and Associated Terms (VIM) by the Joint Committee for Guides in Metrology, online in pdf form here. I found this linked ...

1

First of all, you wrote the equation for $U$ wrong; it should be $r$ instead of $r^2$ in the denominator. However, that typo isn't what the problem is. The problem is that you've overlooked the word "magnitude" in the question. If a negative number is changed to be a different negative number that's closer to zero, then the magnitude of the number has ...

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Strictly speaking the prefix semi means half, but it's often used in the sense of partial. A good example of this would be semiconductor. So semileptonic just means partially leptonic.

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SIS-100/ SIS-300 is an accelerator under construction for FAIR (Facility for Antiproton and Ion Research) in Darmstadt, Germany. see - http://cern.ch/AccelConf/e08/papers/mopc100.pdf I believe, but am not sure, that the -100 and -300 refers to the magnetic rigidity (i.e. Magnetic field * bending radius) of the accelerators, which determines the maximum ...

1

The SIS accelerators are heavy ion accelerators, and the German for heavy ion accelerator is SchwerIonenSynchrotron (my capitalisation), hence the abbreviation SIS. There is more info in this article.

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In mathematics, complex numbers and rotation are intimately related. After rotation $\theta$ in the complex plane, the number $1$ becomes $e^{i\theta}=\cos\theta + i\sin\theta$. Although $e^{i(2n\pi)} = 1 = \cos(0) + i\sin(0)$, you actually moved by $\theta$ and not by $0$. If you rotated something by $\pi$, you could say the angle is now $-\pi$ - but you ...

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