How were electron density clouds established?

[Helicobacter]

Suppose I plan an experiment to sample the position of an electron in an atom.

I pick an arbitrary position that's close to the nucleus. Isn't the probability that I will find an electron at that exact chosen position at anyone moment in time equal to 0, since an electron is thought of being point-like/infinitesimally small? In the probability desnity function Pr(X=x) = 0 for all x in the domain.

How does the electron move around the nucleus? Does it appear at one location as soon as it disappears at another location (in a memory-less fashion), and the previous position does not matter? Or is the movement continuous (like in the Bohr model, just with irregularly shaped orbits)? Or is it pseudocontinuous/discrete, meaning the next position depends (is correlated) with the previous position? If one of the noncontinuous cases reflect the truth, what is the time period until it appears somehwere else?

Also, why does the proton not suck in the electron due to the magnetic attraction?

Regarding the wave-particle duality I am confused as well. What does it mean to be a wave? Does the electron oscillate slightly across the two axes that are perpendicular to the orbit?

 

[Naty1]

Some good discussion here: https://www.physicsforums.com/showthread.php?t=515106

Isn't the probability that I will find an electron at that exact chosen position at anyone moment in time equal to 0,

no...if it were so you'd never locate it...The probability you will find an electron at a particular postion is given by the probability density of the Schrodinger wave wave equation at that point.

How does the electron move around the nucleus? If one of the noncontinuous cases reflect the truth, what is the time period until it appears somehwere else?

For a visual representation, see here:'
http://en.wikipedia.org/wiki/Atomic_orbital#The_shapes_of_orbitals


"Also, why does the proton not suck in the electron due to the magnetic attraction?"

because the electron does not follow classical Maxwell electromagnetic behaviors...it does not radiate energy and fall in as expected classically. ...things in the subatomic realm follow quantum rules...the electron is in a bound state and therefore quantized...but I am not sure WHY that is...not sure anybody knows WHY...

I don't think anyone can derive quantum mechanics from first principles...if so I'd like to see what they are. I would think if we could, we'd know all about quantum gravity.

"What does it mean to be a wave?"

In brief, a wave is spread out over space,...,perhaps all of space.

Here are some related thoughts I've been collecting from various sources that explain WHAT is happening, maybe not WHY: [If you ahve not seen any of these before, be warned they do NOT follow classical (macro observation) "logic". As Richard Feynman said, "Nobody understands quantum mechanics"...but we can describe a lot.

Any wave psi(x) is a superposition of plane waves exp (ikx)….To measure a particle location in an interval, the various plane waves forming psi(x) have constructive interference within that interval and destructive interference outside the interval.

[This is not considered to be a PHYSCIAL wave, but a statistical probability distribution.]

The intervention of a measuring instrument destroys all causal connection between the state of the system before and after the measurement; this explains why one cannot in general predict with certainty in what state the system will be found after the measurement.

A particle, such as an orbiting electron, can be thought of as a resonant cavity, a confined wave, having a discrete series of proper frequencies explaining quantization. (This contrasts with the classical picture of an electron particle orbiting like a moon.)

It is a POSTULATE that the Schrodinger wave equation psi of a quantum system completely defines it's dynamical state.

A particle (or equivalently a quantized wave) in a bound state has a vanishing probability of finding the particle at infinity. The quantization of the energy of bound states is one of the most striking facts of quantum theory. A particle in an unbound state does not remain localized in a finite region...[the electron spreads everywhere like an electromagnetic wave]