Quantum mechanics

The central mystery that quantum mechanics seeks to describe (not explain in a deeper sense) is the structure of the atom. Classical mechanics cannot not properly describe the atom because there is nothing in classical mechanics to suggest that an orbiting electron would not radiate energy and spiral in to the nucleus. Classical theory in fact, predicted that all atoms would immediately destroy themselves in spectacular high-energy blasts of radiation.

Quantum mechanics describes an electron bound to an atom as a three dimensional wave function (eigenstate). The particular physical situation determines what and how many states there are. Eigenstates are useful because what makes one eigenstate different from another usually has a physical meaning but the math required can be a horribly difficult problem to manage. Quantum mechanics describes the absorption and emission of radiation as accompanying transitions "quantum leaps" between eigenstates. Energy therefore exists as indivisible packets, called "quanta". Hence the name: Quantum Mechanics. 

For electron shell diagrams click ...

Schrödinger's model of the atom