I took a degree in nuclear engineering
Of course you can say that Bohr derived the quantized angular momentum by looking at the discrete energy levels since they were known before.
It is exactly what I say
Not only
The Bohr's model is more or less valid for the atom of hydrogen only and just a few others atoms ( including mercury)
It is not even compatible with the atom of helium
For this reason it must be understood as semi empirical model
why does the Schrödinger equation give you an explanation while the Bohr model does not?
You provided yourself the scientific explanation
Let's translate it into a plain spaghetti English
Generally speaking you can describe a physical model using a differential equation
However it does not mean that all the solutions of the equations must have a physical meaning
Having said that, let's write the Schrödinger's equation for the atom of hydrogen
The equation contains the parameter "E" for energy
If you assign to "E" an arbitrary value then the solutions of the equations do not have any physical meaning
Only for some discrete values of E ( the eigenvalues ) the solution of the equation make sense from a physical point of view
This set of E values comply with the the experimental values
In other words for Bohr the quantization of the energy levels is an input for Schrödinger it is an ouput
I suppose there is a difference
Of course electrons are waves. This does not conflict with the probabilistic interpretation.
If you mean some stuff such as the collapse of the wave form well there is still a minority of scientists who believe in this theory ( The great Roger Penrose for example ) but it has been refuted by the vast majority of scientists
Electrons are supposed to be particles even though they dont behave same as the normal particle we are used to
Right or wrong this is the state of art of modern quantum physics
Once again an interesting discussion =).
I agree, at least for us
