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On ``Diagonal'' Coherent‐State Representations for Quantum‐Mechanical Density Matrices

### Abstract

It is proved that every density matrix is the limit, in the sense of weak operator convergence, of a sequence of operators each of which may be represented as an integral over projection operators onto coherent states (in the sense of Glauber) with a square‐integrable weight function. This result is a special case of one that holds for all operators with trace and for overcomplete families of states other than just the coherent states. We prove our more general result, at no cost of complexity, within the more general framework of continuous‐representation theory. The significance of our results for representing traces of operators is indicated.

© 1965 The American Institute of Physics

Received 25 September 1964
Published online 22 December 2004

/content/aip/journal/jmp/6/5/10.1063/1.1704330

http://aip.metastore.ingenta.com/content/aip/journal/jmp/6/5/10.1063/1.1704330

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