**The probability nature of quantum mechanics**

A simple question arises about wave functions
for particles in quantum mechanics: *What is waving?* The interpretation is that
the wave function
**Y**** (x,t) **is related to the probability of observing
the particle at a given position. Specifically, the square of the wave function

The equation one solves to find **Y **is **Schroedinger's
equation**, named after the physicist Erwin Schroedinger who was one of the
founders of quantum mechanics in the 1920s. Schroedinger's equation is a differential
equation which when written in one dimension is:

where

Schroedinger's equation looks like energy
conservation with the twist that the momentum is replaced by a derivative with respect to
the position * x*. As this equation involves two derivatives,
calculus can quickly show that if the potential