The Physical Principles of the Quantum TheoryThe contributions of few contemporary scientists have been as far reaching in their effects as those of Nobel Laureate Werner Heisenberg. His matrix theory is one of the bases of modern quantum mechanics, while his "uncertainty principle" has altered our whole philosophy of science. 
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This excellent book is a cheap way, (< $10 at review time), to get a view of how Heisenberg thought about quantum mechanics circa 1930. The book is constructed from his notes for a series of lectures given at the University of Chicago. The book is about 3/4 text discussing an overview of quantum theories and the experiments that led up to/verified those theories. The last quarter or so is dedicated to laying out the mathematical formalism.
Review: The Physical Principles of the Quantum Theory
User Review  Goodreadsa brief history on experimental ontology of mathematical apparatus. Read full review
Contents
INTRODUCTORY  1 
CRITIQUE OF THE PHYSICAL CONCEPTS OF THE COR  13 
CRITIQUE OF THE PHYSICAL CONCEPTS OF THE WAVE  47 
THE STATISTICAL INTERPRETATION OF QUANTUM  55 
DISCUSSION OF IMPORTANT EXPERIMENTS  66 
Diffraction Experiments  76 
The Experiment of Einstein and Rupp  79 
Emission Absorption and Dispersion of Radiation  80 
THE MATHEMATICAL APPARATUS OF THE QUAN TUM THEORY  105 
The Transformation Theory  123 
The Schrodinger Equation  132 
The Perturbation Method  138 
the Physical  142 
terpretation of the Transformation Matrices  152 
The Corpuscular Concept for Radiation  153 
Classical Theory  157 
b Correspondence Principle and the Method of Vir tual Charges  82 
ri The Complete Treatment of Radiationand Matter  84 
Interference and the Conservation Laws  88 
The Compton Effect and the ComptonSimon Ex periment  92 
Radiation Fluctuation Phenomena  95 
Relativistic Formulation of the Quantum Theory  101 