An introduction to quantum mechanics : from facts to formalism / Tilak Sinha (Narasinha Dutt College, Howrah, India). - First edition. - 1 online resource (xvi, 250 pages) : illustrations
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.
"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"--
9781003090335 1003090338 9781000415643 1000415643 9781000415636 1000415635
10.1201/9781003090335 doi
Quantum theory.
SCIENCE / Mechanics / General
SCIENCE / Quantum Theory
QC174.12 / .S536 2021
530.12