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Full Description
Almost ?fteen years later, and there is little change in our motivation. Mathem- ical physics of quantum systems remains a lively subject of intrinsic interest with numerous applications, both actual and potential. Intheprefacetothe?rsteditionwehavedescribedtheoriginofthisbookrooted at the beginning in a course of lectures. With this fact in mind, we were naturally pleased to learn that the volume was used as a course text in many points of the world and we gladly accepted the o?er ofSpringer Verlag which inherited the rights from our original publisher, to consider preparation of a second edition. It was our ambition to bring the reader close to the places where real life dwells, and therefore this edition had to be more than a corrected printing. The ?eld is developing rapidly and since the ?rst edition various new subjects have appeared; as a couple of examples let us mention quantum computing or the major progress in theinvestigationofrandomSchr. odingeroperators.Thereare,however,goodsources intheliteraturewherethereadercanlearnabouttheseandothernewdevelopments.
Contents
Some notions from functional analysis.- Hilbert spaces.- Bounded operators.- Unbounded operators.- Spectral theory.- Operator sets and algebras.- States and observables.- Position and momentum.- Time evolution.- Symmetries of quantum systems.- Composite systems.- The second quantization.- Axiomatization of quantum theory.- Composite systems.- Scattering theory.- Quantum waveguides.- Quantum graphs.
