Ocean density vs atmosphere density I understand that the density of the oceans on Earth in on average constant regardless of the depth. It is 1020 kg/m^3 at the surface and 1050 kg/m^3 at deep waters.
I understand too that this is not the case with the atmosphere. The density of the atmosphere decreases with height.

Though, I could not find any description in QM, that would describe the difference between the two media, and how they react differently to gravity, and the distance from the center of mass does or does not change their density.
Question:


*

*Is there an explanation why the density of the oceans is (mostly) independent of depth, but the atmospheric density changes with height (is this just because of one is liquid and one is gas)?

*Is there a QM explanation to this (different material) or is this just because of the distance from the center of mass (GR)?
 A: The incompressibility of liquids is due to the fact that they are made of atoms or molecules of finite radius. The atoms in a liquid are constantly in contact with their neighbors, and increasing the density would require that atoms or molecules overlap, which they typically don't do very readily. as such, liquids have an essentially fixed density.
In a gas, the atoms/molecules are not in contact with their neighbors, so the density can vary widely as the distance between one atom/molecule and its neighbors increases or decreases.
No QM or GR is required here.
A: The barometric formula predicting the density curve of the atmosphere is a prediction of classical Newtonian gravity and fluid dynamics, no general relativity required.
The (in)compressibility of gases and fluids is related to the average distance between the molecules in gases compared to fluids, and the distance in fluids is so small that the repulsion of molecules as you try to compress them further is rather strong, while it is rather weak for the "large" distance in gases. This is related to the shape of the Lennart-Jones potential, as John Rennie explains in a bit more detail here.
A: 
What I do not understand is, why is air not one single average
  density, why does density decrease?

Here is a simple analogy that may help understand why the density and pressure at the bottom of the atmosphere is greater than at the top.
Imagine a million of compression springs stacked on top of each other. 
The spring at the bottom will be compressed a lot, because it'll have to counter the weight of the rest of the springs pressing on it from the top. The spring in the middle will be compressed half way, since it'll have to counter the weight of half of the springs. The spring on the top won't be compressed at all.
So we can see that even if the gravity does not change with altitude and all springs weigh the same, the compression of the springs (and their effective density), will be increasing linearly from the top to the bottom.
Of course, the degree (coefficient) of the compression will depend on the ratio between the spring weight and the spring constant: the greater the ratio, the greater the compression.  
A similar thing happens with the water in the oceans and the air in the atmosphere, i.e., we can view a column of water or air as many water or air cubes stacked on top of each other, the degree of their compression (pressure and density) being a function of the ratio of their weight and effective "spring constant".    
