
Chapter 2 0
Some Asymptotic Results
and Formulas
This chapter serves as a very brief introduction to asymptotic methods, which can be used
if the differential equation, system of equations, or problem to be solved contains a small
or large parameter. Examples of such problems include:
1
◦
. The Schr
¨
odinger equation in quantum mechanics. The equation contains Planck’s
constant ~. If we are in a situation where P lanck’s constant can be viewed as a
small parameter, then one can try to solve problems for the Schr¨odinger equation
asymptotically as ~ → 0. This is known as the semiclassical approximation.
2
◦
. The wave equation u
tt
−c
2
∆u = 0 itself does not