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. 

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:

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