From Schrodinger's equation to the quantum search algorithm

The quantum search algorithm is a technique for searching N possibilities in only O(rootN) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. 

This paper describes these steps, which start by discretizing Schrodinger's equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.