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Hamiltonians are calculated to 95% probability.
Think about it, what area is the only area to have 100% chance of containing a particle.
Overall, the set of probabilities for all the places it could occupy is what you're calling the 'cloud'. All these probabilities, of course, add up to 1.
You don't understand in layman terms. Here's proof of that:
originally posted by: liteonit6969
Recently I've been persisting with trying to understand quantum physics and similar theories. To be honest I can understand in lay man's terms but beyond that I'm lost.
"micro" and "macro" are "dumbed down" characterizations, but even a layman should understand that there is precise mathematics behind quantum theory, even if they don't know the precise mathematics. There's nothing in the math that says "micro" or "macro".
As I'm sure many do when reading some "spooky" effects provided by quatum pyshics I have thought long and hard about possible implications of results.
The idea that the micro world acts very much differently to the macro world really annoyed me for this reason. Is the terms of micro and macro not subjective to the observer?
So instead of "micro" and "macro" you can think "buckyballs" and "bowling balls". Note if you had longer than the age of the universe to do the experiment with bowling balls it might be possible according to the math, but of course we don't have that long which is why we say it's not really possible given any realistic experimental conditions.
If this wave-particle duality seems so readily demonstrated, one might wonder why we don't see more examples of this in our everyday lives. Why, for example, don't we see obvious ``particles'' like bowling balls behaving as waves sometimes. The answer to this lies in the very small size of Planck's constant (6.63 x 10^-34 J-s), which implies that wave-particle duality exists most readily at the atomic scale. However, in principle we could illustrate the wave nature of bowling balls by setting up a suitable diffraction experiment. Recall, though, that for significant diffraction to occur that the width of the slits must be of the order of the wavelength being used. For a bowling ball traveling at 1 m/s, this would mean that we would need slits about 10^-34 m wide, which is far beyond today's technology. One could increase this size by reducing the speed of the bowling ball (recall the wavelength of the de Broglie wave is inversely proportional to the speed of the particle). However, to use a slit of about 10^-5 m in width would imply that the bowling ball would have to travel at about 10^-29 m/s, which would mean that it would take a very long time (longer than the age of the universe) to pass through the slit. The conclusion we draw from this is that in our everyday lives we are protected from ``quantum weirdness'' by the smallness of Planck's constant, but that this does occur readily at small length scales and, at least in principle, also applies at larger scales.