Abstract
Summary The motivation for the use of the Green's function (GF) concept in mathematical physics and the diversity of its applications are discussed, with reference to both classical and quantum mechanical problems. First, the impulse response GF is defined and its use is demonstrated in a problem in electrostatics. The connection with the wave response GF is explained and illustrated in an electronics problem. After a review of the use of these concepts in classical problems their unification in quantum mechanics is discussed. An outline of the ideas of quantum field theory prefaces the discussion of the application of GFs to quantum mechanical problems, especially in many-body theory. The two most important mathematical techniques used in the evaluation of GFs are compared.
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