Hello friends, I am a student of VLSI and have initial topics of quantum mechanics in my course work.
I am experiencing some difficulties in understanding the same and i will post my queries here.

Some of my doubts may be silly (as i am going through these topics after 6 years), hence i request for your patience.

To start with, i am quoting a statement by de broglie
(Query 1)

I am experiencing trouble understanding the bold parts.
Please explain it.

Remember chemistry? With that 1s2 2s2 2p6 3s2 3p4 -type description for orbitals? Well those are the quantum integers describing "the stable motion of electrons in the atom". Plug these in the correct shrodinger equation solution (wave function of the selected atom) and you get the geometry for the orbital.

That is what he's saying before the comma. Before QM, the only similar physical phenomena was with waves. For example, one can assign an integer for each musical note (soundwave). That is totally exact and rigorous, it's just easier to say do re mi etc. instead.

What granpa and Dr Lots-o'watts offered -- plus I would say just consider standing wave patterns. The resonant, vibrational frequencies manifest in integer multiples. This is demonstrable macroscopically, and it seems to be a working principle at the submicroscopic scale as well. Of course, the only 'description' of the submicroscopic scale is mathematical, but the math is based on macroscopic analogs, and it produces very accurate predictions wrt instrumental behavior.

Does this help at all? It's the way I, at least begin to, 'understand' it.

I’m only a layman and literally everyone here has more knowledge on QM, but maybe I can help you.

If you look at the picture below, it’s pretty obvious what de Broglie talks about:

This example of the hydrogen atom, shows de Broglie wavelength of one electron, with 7 phases.

As you can see we can only have fully completed phases = integers. It would be impossible for an electron to have 6.5 phases – since it would NOT make a complete "circle"!

Hope this helps.

(Here’s more info on the http://en.wikipedia.org/wiki/Matter_wave" [Broken].)

Do we say that the electron has stable orbits because it is wavelike (as the naive picture below suggests)
or do we say that the electron is wavelike because it has stable orbits.

Good question granpa! Personally – I have no idea. But my feeling is that "picturing" the atom is just a tool (not to go insane ). As I understand this, the http://en.wikipedia.org/wiki/Energy_level" [Broken] in the atom is strongly dependent on these de Broglie "integer phases", since this is the only places where an electron is allowed to "be" (or "orbit"), and in its extension – this is the true source for the quantification in QM... which in turn prohibit the negative electrons to crash into the positive nucleus.

The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.

I dont know what all that means but it seems to show that the wave can in certain situations have macroscopic effects. Notice that the current is a sine wave