Where does the energy for electron movement in orbitals originate?

[scientifico]

Hello, where does the energy that let electrons move inside orbitals came from and are they subject to Coulomb attraction with the nucleus ?

 

[Naty1]

Wikipedia has this introductory explanation

The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency.

http://en.wikipedia.org/wiki/Atomic_orbital

Yes, electrons are attracted by protons...and they also have a much smaller gravitational attraction. No one knows exactly WHY there is the electromagnetic force [nor the other forces nor gravity] nor, for example, why the electron has the exact charge and mass we observe. For a 'particle' to absorb a photon you need internal degrees of freedom which can be excited. In an atom it's not the [bound] electron alone that absorbs the energy of an incoming photon but the whole atom. The proton-electron system as whole can absorb the energy of a photon unlike a single free electron The additional degrees of freedom are provided by the substructure of the proton-electron system, i.e. the energy levels of this system. Again even in the atom it's not the electron that absorbs the photon, it's the whole atom; otherwise energy-momentum conservation would be violated.

Think of a violin string as an analogy: the ends are constrained, so it can have only certain tones...certain vibrational patterns and associated energies. it's energy levels are constained to certain values...it's degrees of freedom are limited.

Another helpful analogy is to think of the electron as a wave...when it's in free space the wave is everywhere, it extends all over the place. But when attracted by a proton in a nucleus, for example, that wave is now localized...it's constrained and so its different from the free space case. And the constraint is also modified by the presence of other electrons and additional protons. Since the energy is contained in the wave, changing it's configuration via the presence of nearby particles changes the wave characteristic and likely energy levels. It's very unlikely for the electron to be found between allowed energy levels.

In contrast, a free electron can take on any energy level...any velocity, for example. But when it is part of an atom or a larger structure, it's constrained...it's degrees of freedom are determined and limited by the whole structure. So an electron's energy levels and degrees of freedom are determined by the numbers of protons in the nucleus as as well as the particular structure of a lattice, as examples. The Schrödinger wave equation describes these.