Operational Quantum Physics
Abstract
This tome is a formal presentation of the unsharp observable approach to quantum mechanics using the positive operator valued (POV) concept of an observable. It is intended for philosophers and mathematicians as well as physicists. This is a very formalistic book. There are, however, portions that should be read by all experimentalists performing quantum mechanical studies as well as graduate students completing their first graduate year quantum mechanics course. If we interpret quantum mechanics as making statistical predictions on the results of states prepared in identical fashions, we will often find that the observed probabilities are nearly, but not exactly, the expected 1 or 0 for measurements that are expected to always give the same result. Hence, rather than demanding sharp measures with probabilities of exactly 1 or 0, quantum mechanics allows a reasonable interpretation of unsharp results of nearly 1 or nearly 0. As the authors point out in chapter II, POV measures and the associated unsharp measures are not essential for an interpretation of quantum mechanical results. However, more sharp variables, and hence a larger Hilbert space, will be needed than are required by the unsharp approach. Also, the theoretical interpretation will often not be as straightforward with only sharp observables. As I have previously stated, all graduate students, both those of a theoretical and those of an experimental bent, should read parts of this book (after they have completed a…
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