In thIS thIrd volume of A Course In Mathematlcal Physlcs I have attempted not sImply to Introduce aXIoms and derIve quantum mechanics from them, but also to
progress to relevant applIcations ReadIng the aXIomatic lIterature often gIves one
the ImpressIon that It largely consIsts of malang refIned aXIoms, thereby freeIng
phYSICS from any trace of down-to-earth resIdue and cutting It off from sImpler
ways of thInkIng The goal pursued here, however, IS to come up WIth concrete
results that can be compared wIth expenmental facts EverythIng else should be
regarded only as a sIde Issue, and has been chosen for pragmatic reasons It IS
precIsely wIth thIS In mInd that I feel It appropnate to draw upon the most modern
mathematical methods Only by theIr means can the logIcal fabrIc of quantum
theory be woven wIth a smooth structure, In theIr absence, rough spots would
InevItably appear, especIally In the theory of unbounded operators, where the
details are too Intncate to be comprehended easIly Great care has been taken to
buIld up thIS mathematical weaponry as completely as possible, as It IS also the
basIc arsenal of the next volume ThIS means that many proofs have been tucked
away In the exerCIses My greatest concern was to replace the ordInary calculations
of uncertaIn accuracy with better ones havIng error bounds, In order to raIse the
crude manners of theoretical phYSICS to the more cultivated level of experImental
phYSICS.