Journal of Mathematical Physics

Projection operator techniques in physics

Wesley E. Brittin, A.Y. Sakakura

Published May 1, 1984• 6 citations

Abstract

A systematic account of projection operators (projectors) and orthogonalization techniques together with applications to selected areas of physics is presented. This unified approach is shown to have advantages over other approaches in that the mathematical statements are more precise. The mathematical level, however, is aimed at the practicing physicist and lies between rigorous mathematics and current use in physics. Further, the techniques presented have practical applications as is demonstrated by examples in the quantum theory of measurement, in the relationship between second quantization and configuration space techniques, and in an account of generalized Wannier and Bloch functions. Attention is paid to the problem of construction of orthogonal projection operators (orthogonal projectors). The construction of orthogonal projectors even in approximate form would allow the solution of many practical problems ranging from the eigenvalue spectrum problem to the construction of states for many-body systems. One can almost say that any problem in quantum mechanics can be formulated as a problem involving the construction of projectors.

DOI: 10.1063/1.526284

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