# Tag Info

2

The difference between absolute values and squaring is purely a matter of convenience: it's less of a headache to deal with squares, than with absolute values because of the sign of what's inside the absolute value. If you're evaluating an integral, as you would be if you're after expected value, then there's no need to consider when $D$ is positive or ...

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This came to my mind after reading some introduction to maximum entropy probability distributions. Independence can be derived from the following four assumptions: (1) average momentum of particles inside the box is fixed at 0 (2) average kinetic energy of particles inside the box is fixed (3) the gas velocity distribution must be maximum entropy ...

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First of all you have to consider that there's an electric force (Coulomb) between nucleus and electron, so, from a classical point of view it seems reasonable that electron "wants" to stay as closer as possible to the nucleus (they respectively attract). Now it's clearly impossible that electrons could reach nucleus, from an intuitive view points you can ...

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The short answer to your question is that in "nature;" energy, forces, and particles, operate in such a way that the energy or force needed to reach some kind of "stability" (equilibrium), is minimized. In the case of an electron, its "ground state" is the most stable, so the probability of "finding" it there, is very high (if not the highest).

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One purpose of using $\Psi$ rather than just the probability density is to match observation. Dealing only with probability density isn't sufficient. Imagine you can send particles through two adjacent slits toward a detector screen. You'll find an interesting pattern that looks like an interference phenomenon is happening. This is called the double slit ...

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You will almost never encounter a calculation that is intended to account for every detail of a phenomenon with perfect accuracy. That isn't possible, and in fact many times adding more detail to a calculation only takes away from the insight it grants. Why make a complicated calculation when a simple one tells you everything you want to know? Gamow is ...

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Some kinds of mutation provide an example of this kind of indeterminacy. UV light can be bad for our health. One of the reasons is that, when we are exposed to sunlight, UVB photons are absorbed by double bonds in pyrimidines, which break open, become reactive, and dimerize (photo-dimerization). This damages the DNA in the same way that it would damage a ...

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Yes. $D$ refers to the same quantity in both expressions. In fact, equating them is one way to derive the Einstein-Smoluchowski relation. See the last section of these notes for more details.

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(a) Your answers are correct. (b) Yes,it is simpler to write out the wave packet in the momentum basis. (This is effectively equivalent to working out the three-dimensional Fourier transform of the given Gaussian wave packet in position basis.)

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Wigner function is not a true probability distribution as it may possess negative values, particularly when the quantum state has no classical analogue.

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This is a matter of QUALITY and aging of the "fair" coins (long-aged one can be researched for instance in museums), the entropy will grow because of friction, the process of aging, bluring and deleting of signs i.e. tails/heads will continue during very long tossing, the coin has limited life which is usually not mentioned in ideal models. The question is ...

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As far as I am aware, we are only able to speculate about these other "Universes" in the sense that they represent an aggregate of potential (indeterminate) wave functions relating to what events may occur in the time direction known as "future". Or might have occured in the "past" but didn't in this universe. Every time you toss a coin and look at it, that ...

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