Operators and Canonical Quantization

Abstract

One essential feature of quantum theory should have become apparent by now. And that is the central role played by linear operators, which we shall merely call operators. We assume that the reader is familiar with vector spaces and linear transformations from linear algebra of finite dimensional spaces. In this book the vector space can be infinite dimensional. And we say ‘operator’ instead of ‘transformation.’ The field of scalars will usually be the complex numbers, in which case we are then considering complex vector spaces. First as a quick refresher here are some basic definitions.