Mathematical Foundations of Quantum Mechanics

Title Page......Page 1
PREFACE......Page 5
CONTENTS......Page 9
The origin of the transformation theory......Page 11
The original formulations of QM......Page 14
The equivalence of the two theories......Page 26
Hilbert space......Page 36
The definition of Hilbert space......Page 42
The geometry of Hilbert space......Page 54
Digression of the conditions A-E......Page 67
Closed linear manifolds......Page 81
Operators in Hilbert space......Page 95
The eigenvalue problem......Page 110
Continuation......Page 116
Initial considerations......Page 127
Digression on the existence and uniqueness......Page 153
Commutative operators......Page 178
The trace......Page 186
The statistical assertions of QM......Page 204
The statistical interpretation......Page 214
Simultaneous measurability......Page 219
Uncertainty relations......Page 238
Projections as propositions......Page 255
Radiation theory......Page 262
The fundamental basis of the statistical theory......Page 303
Proof of the statistical formulas......Page 322
Conclusions from experiments......Page 336
Measurement and reversibility......Page 355
Thermodynamical consideration......Page 366
Reversibility and equilibrium problem......Page 387
The macroscopic measurement......Page 406
Formulation of the problem......Page 425
Composite systems......Page 429
Discussion of the measuring process......Page 445