Quantum mechanics is the field of physical science that deals with the behavior of matter on the atomic and subatomic levels. At first, matter was thought to behave as very small, minute particles, little pieces of solid material. But, as the study of the atom and it's subatomic structures progressed, discoveries were made that revealed matter also possesses behavioral qualities more related to wave-like patterns. This opened up a whole new field of study, called quantum physics, or quantum mechanics, that related the interchangeable qualities matter possesses between particle behavior and wave behavior. There is no one singular quantum mechanics equation, but here is the equation for the "uncertainty principle"
(change in x)(change in p) is greater than or equal to h/2
The link I have provided below gives several other formulas that might be of interest, as well as a detailed development and history of quantum mechanics.