When it was an era of classical mechanics we used to believe in the Bohr's atomic model. It interpreted electrons as particles (although I couldn't understand how come Bohr who interpreted electron as a particle, formulated an equation for electron's angular momentum which shows its mathematical proof to be a wave.) and are revolving around nucleus with their own particular energy for each orbit. This solved drawbacks of Rutherford's model which lacked to explain electron's stability. Bohr suggested that electrons could only have certain classical motions:
Electrons in atoms orbit the nucleus.
The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics. The Bohr model of an atom was based upon Planck's quantum theory of radiation.
When Bohr restricts an electron's orbiting distance from nucleus by providing only a certain set of distances, isn't it called quantization? And why this set of laws?
Why does one restrict a particle's motion to some discrete set of distances? Is it to provide a theory on the particle's stability?
When one says the electron behaves like a standing wave, which can be compared with waves on string, then from where those nodes arise in the case of electrons revolving around a nucleus?
Simply when one compares first harmonic of wave on a string with electrons moving around nucleus, from where do the nodes shown in the figure arise in case of orbiting electron?**
Let me say, electron, a wave, which has certain wavelength and frequency owing to its distance from nucleus (energy of different electrons at different distances from nucleus differ) executes a harmonic based on its energy. So as we move towards some nth harmonic, the trajectory becomes complicated. Is it that case? Am I wrong? But still I can't understand the arising of nodes..
How do s,p,d and f orbitals (are they the way in which the electron, a wave, moves around nucleus as a function of time?) exist without interfering each other? I mean, an atom is so small. Don't they mix up, i.e. superpose? Is it that the n+1 nodes in an arbitrary orbital are there because of its preceding orbital?
Also, when I look at the 3D shape of d orbital esp. the one with ring (d-z^2), I feel it's so complicated. How do they arise?! What are those +/- written over the orbitals?