The Schroedinger Equation (SE) is a linear differential equation. This
means that if Psi1(x,t) and Psi2(x,t)
are solutions to the SE then a linear combination of Psi1(x,t)
and Psi2(x,t) is also a solution. This
property of the SE is known as the principle of superposition. The
simplest solution to the SE for the free particle is a plane wave solution
called a deBroglie wave. By adding
together free particle solutions to the SE, a localized wave packet may be
obtained.
This set of exercises will investigate the representation of a localized free particle,
and its motion, by a wave function.
Section 1a 

Complex numbers. Phasors 
Section 1b 
Complex plane waves. DeBroglie waves 

Section 2a 
Properties of traveling waves 

Section 2b 
Superposition. Group and phase velocity 

Section 2c 
Localized wave packets 

Section 2d  Dispersion  
Section 3 
Time evolution of a Gaussian wave packet 

Section 4 
Uncertainty relations 
Refer to the Chapter 7 in Modern Physics by Bernstein, Fishbane and Gasiorowicz:
© 2000 by PrenticeHall, Inc. A Pearson Company