Introduction to Quantum Mechanics: Mathematical Foundations and Physical Applications — Expanded Edition

A rigorous, progressive, and self-contained introduction to quantum mechanics - now in an expanded edition.From Planck's hypothesis in 1900 to the Schrödinger equation and beyond, this book traces the historical foundations of quantum theory, develops its mathematical framework, and applies its principles to the most important physical systems.What's inside (23 chapters in 4 parts): Part I - The Quantum Revolution: The crisis of classical physics, blackbody radiation, the particle nature of light, matter waves, and the uncertainty principle.Part II - Mathematical Foundations: Vector spaces, Hilbert spaces, linear operators, eigenvalues and the spectral theorem, and Dirac notation.Part III - Quantum Mechanics: The postulates of quantum mechanics, the Schrödinger equation, expectation values and probability current, the free particle and confinement, the harmonic oscillator, one-dimensional potentials, angular momentum, and the hydrogen atom.Part IV - Advanced Topics (new in this edition): Spin and total angular momentum, identical particles and the Pauli exclusion principle, time-independent perturbation theory, the variational method, the WKB approximation, and one-dimensional quantum scattering.Features: Ideal for university students in Physics, Engineering, and Chemistry seeking a solid bridge between classical physics and the fascinating quantum world.- Complete proofs and detailed derivations- Worked examples in every chapter- Exercises classified as Basic, Intermediate, and Advanced- Six appendices covering Fourier transforms, special relativity, physical constants, equation summaries, special functions, and a historical chronology- A rigorous yet accessible academic approach