The Schrodinger Equation
In 1926 Erwin Schrodinger proposed an equation which describes completely the time evolution of the matter wave ??
( - (h2 / 2m) ? 2 + V) ????i h (d? /dt)
where m = characteristic mass of “particle”
V = potential energy function to describe the forces
Given the force, find motion Given potential, find wave
F = ma = m (d2x/dt2) (- (h2 / 2m) ?2 + V) ????i h (d? /dt)
solution: x = f(t) solution: ? = f(x,t)
Note: Schrodinger’s equation is more difficult to solve, but it is just as well-defined as Newton’s. If you know the forces acting, you can calculate the potential energy V and solve the Schrodinger equation to find ?.