Quantum mechanics and atomic bonding I'm learning quantum mechanics in high school this year, and I have several doubts. I've done my research on various websites but my understanding is still fuzzy. I understand that when I punch a wall or sit on a chair I don"t go through it due to quantum degeneracy pressure. I've studied the Pauli exclusion principle, but here"s my first question: 


*

*What exactly is quantum degeneracy pressure? I've read answers that say "Atomic orbitals resist squishing", and the like, but I don"t understand why.

*If orbitals resist squishing, why do covalent bonds form? 
From the Wikipedia picture of a H2 bond it seems like the s orbitals of the individual atoms were squished from a circle(2-D) to an ellipse. How do we know when this squishing results in a lower energy state and when it doesn't? If the wall was made of atoms that didn't have an octet and my hand too would my hand bond with the door when I punched it?
 A: The degeneracy pressure does not directly apply here, I think. It will be important for neutron stars. The particles that matter is made up with (electrons, protons, neutrons) all have spin 1/2. That means that they are fermions.
The wavefunction, which contains all the information about the system, has so change its sign when two particles are exchanged. Since particles of the same kind are indistinguishable, that means two particles cannot be in the exact same quantum state (something like ”spot”). That means that even if you compress something, the neutrons will still not fit into a single spot. That will give you a neutron star, where the degeneracy pressure works against its collapse.
The fact that you do not fall through the chair should just be the electromagnetic repulsion. The electron shells of various atoms repel each other. When you from a covalent bond, the wavefunctions of both atoms overlap. Since the electrons are indistinguishable, that will cause them to spread between the two nuclei.
If you look at the overlapping wavefunction, you find eventually that there are combinations with more and with less energy. See the $\sigma$ and the $\sigma^*$ orbitals in $\mathrm H_2$. Both electrons will go into the $\sigma$ molecular orbital which has lower energy. Therefore, it will form a covalent bound. In $\mathrm{He}_2$, there two more electrons, which just have to occupy the $\sigma^*$ since there is no other molecular orbital around. Since that has an energy which is too high, it is anti-binding. The total energy in the bond is no less than for the individual atoms, so there will not be any bonding.
Your hand and the wall is not likely to bond as a macroscopic bond, since they are just that big. But I could imagine that individual atoms or molecules bind to some of the wall.
