After a quarter century of discoveries that rattled the foundations
of classical mechanics and electrodynamics, the year 1926 saw the
publication of two works intended to provide a theoretical
structure to support new quantum explanations of the subatomic
world. Heisenberg's matrix mechanics and Schrodinger's wave
mechanics provided compatible but mathematically disparate ways of
unifying the discoveries of Planck, Einstein, Bohr and many others.
Efforts began immediately to prove the equivalence of these two
structures, culminated successfully by John von Neumann's 1932
volume "Mathematical Foundations of Quantum Mechanics." This forms
the springboard for the current effort. We begin with a
presentation of a minimal set of von Neumann postulates while
introducing language and notation to facilitate subsequent
discussion of quantum calculations based in finite dimensional
Hilbert spaces. Chapters which follow address two-state quantum
systems (with spin one-half as the primary example), entanglement
of multiple two-state systems, quantum angular momentum theory and
quantum approaches to statistical mechanics. A concluding chapter
gives an overview of issues associated with quantum mechanics in
continuous infinite-dimensional Hilbert spaces.
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