Time dependence of quantum states is governed by Schroedinger's time dependent equation of motion, , in which the Hamiltonian is a differential operator on functions of position through the prescription for the momentum operator: . In applications, the intial wave function is known, Y(x,0), and one seeks the wave function at later times, Y(x,t). That is, the time dependent equation of motion is a partial differential equation with initial conditions.
Stationary states are the energy eigenstates, Hy(x) = Ey(x); solutions of the time independent Schroedinger equation.
Other states are non-stationary. We know the stationary states of the the particle in a
box system: . Suppose
that the following is given as the initial state for the particle in a box.
For such a state, the probability distribution for the particle is not constant. The following is a "movie" showing the evolution of this state with time.
click on the image to view the movie.
The methods for solving such problems are presented in these pages. UNDER CONSTRUCTION.
Created or up-dated 08/03/99
by R.D. Poshusta