This book originated with a course I taught at UC Berkeley during the spring
of 2003, with class notes taken by my colleague Lawrence C. Evans. Various
versions of these notes have been available on-line as the Evans-Zworski
lecture notes on semiclassical analysis and our original intention was to use
them as the basis of a coauthored book. Craig Evans’s contributions to the
current manuscript can be recognized by anybody familiar with his popular
partial differential equations (PDE) text [E]. In the end, the scope of the
project and other commitments prevented Craig Evans from participating
fully in the final stages of the effort, and he decided to withdraw from
the responsibility of authorship, generously allowing me to make use of the
contributions he had already made. I and my readers owe him a great debt,
for this book would never have appeared without his participation.
Semiclassical analysis provides PDE techniques based on the classical-
quantum (particle-wave) correspondence. These techniques include such
well-known tools as geometric optics and the Wentzel–Kramers–Brillouin
(WKB) approximation. Examples of problems studied in this subject are
high energy eigenvalue asymptotics or effective dynamics for solutions of
evolution equations. From the mathematical point of view, semiclassical
analysis is a branch of microlocal analysis which, broadly speaking, applies
harmonic analysis and symplectic geometry to the study of linear and non-
linear PDE.
The book is intended to be a graduate level text introducing readers
to semiclassical and microlocal methods in PDE. It is augmented in later
chapters with many specialized advanced topics. Readers are expected to
have reasonable familiarity with standard PDE theory (as recounted, for
example, in Parts I and II of [E]), as well as a basic understanding of linear
functional analysis. On occasion familiarity with differential forms will also
prove useful.
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