Time Dependence of Quantum States.



Time dependence of quantum states is governed by Schroedinger's time dependent equation of motion, wpe5.gif (1480 bytes), in which the Hamiltonian is a differential operator on functions of position through the prescription for the momentum operator: wpe6.gif (1083 bytes). 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: wpeA.gif (1520 bytes) . Suppose that the following is given as the initial state for the particle in a box.
wpeC.gif (1581 bytes)
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.

wpeF.gif (2529 bytes) 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
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