An Introduction to Quantum Mechanics: From Facts to Formalism

ISBN-13: 9780367547073 / Angielski / Twarda / 2021 / 250 str.

Tilak Sinha

Opis

This book offers a constructive approach to the inner product space formulation of Quantum Mechanics as opposed to inductive approaches based on intuitive associations or blatant axiomatic approaches. It strives to explain the purpose and meaning of the mathematical framework used in the standard description of Quantum Mechanics.

Spis treści

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 QM. Professor Funnyman’s Ghosts. An experiment with Bullets. Elementary Concepts in QM. Notation. The Laws of QM. The Quantum State Redefined. States as Vectors. Vectors in Cn. Towards a Formal Description of QM. Vector Spaces and Inner Product Spaces. The Postulates of QM – Version. Observables as Operators. Linear Operators. Describing Observables by Linear Operators. The Postulates of QM – Version. Quantization. Expectation Values. Imprecise Measurements and Degeneracy. Precise and Imprecise Measurements. Postulates of QM - Version 3. Complete and Incomplete Measurements. Commuting Operators. Compatibility and Commutativity. Time Evolution of Quantum Systems. Unitary Operator. Time Evolution of Quantum States. Postulates of QM - Version 4. The Programme in QM. Solving Schrödinger Equation. Continuous Spectra. Description using Function Spaces. Modified Postulates. Quantization of Systems with Classical Analogues. Three Classic Eigenvalue Problems. Harmonic Oscillator. Angular Momentum. Hydrogen Atom. QM of Composite Systems. The Meaning of a Composite System. Tensor Product Spaces. Description of Composite Systems. Interactions between Subsystems. Measurement on a Subsystem. Examples of Composite Systems. Identical Particles. A Probability. Preliminary Background. Probability in the Frequentist Interpretation. Alternative Interpretations. Formal Description. B Linear Algebra. Vector Space. Inner-product space. Linear Operators. Eigen Systems. Direct Sum of Subspaces. Tensor Product Spaces. Bibliography. Index.

O autorze

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.