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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
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
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Publisher Resources

ISBN: 9781466581494