Schrodinger's wave equation is used to model particles as waves -- waves of what it's not known, but probability is related. Although the meaning behind this equation (and all of quantum physics) isn't really understood, it's enormously successful. And knowing it, and knowing how simple it is, is an odd feeling -- an awe being able to see the universe at a number of levels.
A history of the wave equation: "Classical physics -- that is, Newtonian mechanics and Maxwell's theory of electromagnetism -- seemingly accounted for all observed natural phenomena. It was a deterministic universe. The planets, eternally whirling with their inscrutable precision; the ebbing and flowing of the sea's tides; the oscillations of a pendulum; the way bodies exchange energy and momentum; waves of light propagating through space -- do they all not obey a deterministic model? Some claimed that given the initial conditions of the universe, all of its future behavior could calculated. Alas, as so often occurs in science, a crisis arose that was fatal in nature to classical physics: it failed to account for certain important phenomena. This was the ultraviolet catastrophe".
75 years of the Schrodinger's wave equation (which is rich in links) celebrates the Erwin Schrodinger too. It seems he was a wide thinker: "While in Dublin, Schrodinger also published 'What is Life?' where he claimed that cellular function may be explained according to the laws of thermodynamics; he wrote that the basis of life could be understood through chemical and physical properties. (Although this major aspect of his discourse was later proven to be incorrect, 'What is Life?' still became an intellectual component of the groundbreaking work regarding the function of DNA performed by Crick and Watson.)"