Dark matter/dark energy isn't so much derived from quantum mechanics. Basically the idea comes from a couple of observations taht couldn't otherwise be accounted for. One is that the universe is expanding at an increasing rate. With all our models and how we thought things worked, the expansion should be decelerating, but we observed that it is actually increasing. This acceleration of the expansion needs energy. Also, if we do the math for the rates of expansion and acceleration and such, and then do the math for how much matter/energy (the same thing, just different forms) is observable in the universe, the numbers don't match.
So the universe's expansion is accelerating with an unknown energy source, and the mass/energy observable in the universe is nowhere near enough to account for the rate of acceleration and the energy required. So these ideas combined to form the idea of dark matter/dark energy: the remainder that makes the equations work right, because the things we observed don't add up to a conservation of energy. It's called "dark" because we can't observe it, it's never been observed directly, so it's called dark.
We can see many effects of it though: precise measurements of planets/systems/galaxies etc. also deviate from the observable physics the same way the universe as a whole does, so scientists have been able to determine some properties of dark matter/energy by how these systems deviate from their expected behavior if dark matter/energy wasn't present.
So we don't know what it is or where it comes from, and can't derive its origin or how it works. So it's basically an idea that was created to try to make things add up, to try to make the left hand side of the equation equal the right hand side; we know some things about it because we can observe how it affects objects in the universe, even if we can't observe it (whatever it is) directly.
