Introduction to 
QM  Wave Packets

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. 

Refer to the Chapter 7 in Modern Physics by Bernstein, Fishbane and Gasiorowicz:

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