# Time Dependence of Quantum States.

preview

## Contents

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.

## Preview. Solution for a PIB state.

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**.

- R. Liboff,
*Introductory Quantum Mechanics* [Holden-Day, 1980]

Created or up-dated 08/03/99
by R.D. Poshusta