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 following chapter sections in Modern Physics for Scientists and Engineers by Taylor, Zafiratos, and Dubson:
- Chapter 6, Sections 6-6 through 6-10
- Chapter 7, Sections 7-3 and 7-7
