1st Edition
An Introduction to Quantum Mechanics From Facts to Formalism
Preface. Prologue. Theoretical Framework - A Working Definition. What is a theory? Formal Description of a Theory. Abstraction and Generalization. Philosophy and Fundamental Theorem. Theory vs Theoretical Framework. The Empirical Basis of Quantum Mechanics. Professor Funnyman’s Ghosts. An Experiment with Bullets. Basic Concepts in Quantum Mechanics. Notation. Laws of Quantum Mechanics. The Quantum State Redefined. States as Vectors. Vectors in Cn. Towards a Formal Description. Vector Spaces and Inner Product Spaces. Postulates of Quantum Mechanics – Version 1. Observables as Operators. Linear Operators. Describing Observables by Linear Operators. Postulates of Quantum Mechanics – Version 2. Quantization. Expectation Values. Imprecise Measurements and Degeneracy. Precise and Imprecise Measurements. Postulates of Quantum Mechanics - Version 3. Complete and Incomplete Measurements. Commuting Operators. Compatibility and Commutativity. Time Evolution. Unitary Operators. Time Evolution of Quantum States. Postulates of Quantum Mechanics - Version 4. The Programme in Quantum Mechanics. Formal Solution of Time Evolution. Continuous Spectra. Description using Function Spaces. Modified Postulates. Quantization of Systems with Classical Analogues. Three Archetypal Eigenvalue Problems. Harmonic Oscillator. Angular Momentum. Hydrogen Atom. Composite Systems. The Meaning of a Composite System. Tensor Product Space. Description of Composite Systems. Interactions between Subsystems. Measurement on a Subsystem. Examples of Composite Systems. Identical Particles. Probability. Preliminary Background. Frequentist Interpretation. Alternative Interpretations. Formal Description. Linear Algebra. Vector Space. Inner Product Space. Linear Operators. Eigen Systems. Direct Sum of Subspaces. Tensor Product Space. Bibliography. Index.
Biography
Tilak Sinha is an Assistant Professor in the Department of Physics at Narasinha Dutt College, Howrah, India. He did his PhD on nonperturbative aspects of quantum field theory from Saha Institute of Nuclear Physics, Kolkata, and held a research position in the University of Wuppertal, Germany before joining Narasinha Dutt College in 2007. His interests include ontological and epistemological issues in the foundations of Quantum Mechanics, Quantum Field Theory, and Physics Education.
