http://en.wikipedia.org/wiki/Bohr_model#Electron_energy_levels


Hey I study physics. That 14 years old story was a joke (did nobody get that?). What do you study?


Okay, see the above link. It took me like five seconds to find it. I really don't get where you get that claim from. The Bohr model gives you the frequencies. Via E=hf you get the energy levels. You even explained that yourself o.O. But I'll try again: no matter how Bohr came to the conclusion, he sais that angular momentum is quantized. From that or alternatively from requesting a continuous wave circle (with the electron's de Broglie wavelength) you get discrete orbits. The frequency of these orbits give you the energy levels via E=hf. So the explanation for the discrete energy levels in the Bohr model is the quantized angular momentum or, alternatively, the continuous wave about the nucleus (standing wave). Of course you can say that Bohr derived the quantized angular momentum by looking at the discrete energy levels since they were known before. But that doens't matter. The Bohr model requires the quantized angular momentum to describe the energy levels. Whether or not this explanation is true does not matter. Neither does it matter how Bohr developed his ideas. Nowadays, the Bohr model is derived from the quantum rule for angular momentum, and that's where the discrete energy levels come from.


Again, to summarize: I don't know what Bohr did. The Bohr model though gives the explanation. It sais that all other orbits give no standing wave and thus are forbidden.


In fact the Schrödinger equation is a postulate so it can hardly qualify as an explanation, if I follow your argumentation. For me, though, it gives an explanation (why does the Schrödinger equation give you an explanation while the Bohr model does not? Both are just theories...).


What do you mean with stable?
Ok, time to use the knowledge from the book I read when I was fourteen. JOKE
The time-independent SE is a differential equation. If you plug in the hamiltonian for a Coulomb potential, which is spherically symmetric in the case of a hydrogen-like atom (which is the only one you can solve analytically anyway), you can factorize the wave function into a radial and an angular part. The angular solutions for all spherically symmetric potentials are the sperical harmonics Y_lm, where l is just the angular momentum quantum number and m its z-component (or, alternatively, its magnetic quantum number). For the radial part you get laguerre-polynomials P_nl, where n is the energy quantum number. The energy of this state now can be measured with the hamiltonian and are just its eigenvalues.


Of course electrons are waves. This does not conflict with the probabilistic interpretation.


No. Nothing is moving. Hydrogen wave functions are completely stationary, there is absolutely no time dependence involved (see my derivation above, you use the time-independent SE).

Once again an interesting discussion =).