Explanation of covalent bond from physics point of view?

We can explain ionic bond as the force between charged particles due to Coulomb electrostatic law. This got me wondering how is then covalent bond explained purely in terms of physics?

• why the deselection? Jun 20 '19 at 6:36
• Possible duplicate of What gives covalent bond its strength? Jun 20 '19 at 6:53
• @StéphaneRollandin I think my question is different because it questions the existence of a covalent bond given the law of physics (i.e. coulombs law) because it wasn't apparent to me (unlike the ionic bond). I am satisfied with the answer presented. Jun 20 '19 at 10:23

Covalent bonding is a quantum-mechanical phenomenon that can't be explained classically. The basic idea can be demonstrated in the case of a hydrogen molecule if you think of the electrons as two particles in a box. By joining the two hydrogen atoms together into a molecule, you make the "box" twice as long. Let's pretend that this is a rectangular box. Lengthening the cubical box into a $$2\times 1 \times 1$$ box makes the wavelength along the long axis twice as big. By the de Broglie relation $$p=h/\lambda$$, this reduces the momentum in that direction by a factor of $$2$$, which makes the associated kinetic energy $$1/4$$ as much. The lowered energy makes the system more stable. To pull it apart, you would need to add energy.