please note that I am a high school student trying to understand the quantum model of the atom; I have only the most basic understanding of quantum mechanics.
I am trying to comprehend the wave nature of electrons in atoms but I am unsure on a number of things.
what is meant by a probability cloud of electron(s)? does this mean that the electron is rapidly moving inside the probability cloud/ orbital, present in some regions for a longer time than in others, or is it sort-of smeared throughout the orbital until it is observed?
if an electron exists as a stationary wave around an atom, then what is "waving"? mechanical stationary waves, for example, consist of displacement oscillating with amplitudes that vary with position. What physical quantity is actually oscillating here? Surely, the electrons themselves aren't moving up and down, are they?
the following excerpt is taken from https://en.wikipedia.org/wiki/Atomic_orbital
The electrons do not orbit the nucleus in the manner of a planet orbiting the sun, but instead exist as standing waves. Thus the lowest possible energy an electron can take is similar to the fundamental frequency of a wave on a string. Higher energy states are similar to harmonics of that fundamental frequency.
The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron. The charge on the electron acts like it is smeared out in space in a continuous distribution, proportional at any point to the squared magnitude of the electron's wave function.
IF theese standing waves are probability waves, how can they be related to the discrete energy levels? morever, how can the charge be smeared out if the electrons themselves are not?