I've heard this in many quantum mechanics talks and lectures, nevertheless I don't seem to grasp the idea behind it.
What I mean is, at which point is that our modern understanding of quantum mechanics led to a technological development so fundamental for today's computers that we could not have got it working other way?
Why is it not enough with Maxwell, Bohr, Lorentz, (Liénard)?
Best Answer
The reason is very simple. Computers depend on electronics. Even the first diodes and triodes that the first bulky computers were made up of depending on the quantum mechanical nature of matter. The present ones with the chip technology are directly dependent on energy levels and bands of conduction etc in the electronics used. Semiconductivity is a quantum mechanical phenomenon.
Edit after the editing of the question
The crucial point where quantum mechanical calculations became necessary was with the use of transistor technology, which has morphed to chip technology. It was with the invention of the transistor that control of quantum mechanical calculations was necessary for the leaps in progress we have made. For the vacuum tube computers, it was not necessary except for explaining the tubes existence. The chip designs have reached the point of even needing to foresee the Casimir effect (QM vacuum between charged plates).
Maxwell is not enough because the classical theory cannot explain atoms molecules and solid state. Bohr is not enough because the primitive calculations could not be used in complicated lattices. Lorenz is irrelevant for solid state physics, the energies of the ions and electrons are low.