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Or in other words which forces keep electrons in orbitals and prevent it from flying away or crashing into the nucleus according to modern understanding?

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[–] [email protected] 6 points 3 months ago (2 children)

So: Because an electron with an exactly defined position must have infinite kinetic energy

There are an infinite number of velocities I can use to get up off the couch right now.

That does not mean that I will get up off the couch at infinite velocity.

[–] [email protected] 10 points 3 months ago* (last edited 3 months ago)

Yes, there are an infinite number of velocities you can use, but if you look at their distribution, you'll find that it quickly goes to zero somewhere around 1-2 m/s, so the expectation value of the velocity is convergent.

If you have an object with a velocity taken from a distribution that doesn't approach zero sufficiently fast as the velocity goes to infinity, the expectation value diverges. A simple example would be a person that would be half as likely to get up at a velocity of 2 m/s as 1 m/s, and half as likely to get up at 4 m/s as 2 m/s, etc.

The more mathematical version of the same argument is to compute the kinetic energy of a particle whose wavefunction is a delta pulse (i.e. a particle whose position is exactly defined), and you'll find that the particle has infinite energy.

[–] [email protected] 1 points 3 months ago

You choose a velocity from an infinite number of options, but the electron exists in a superposition of all those options.