CONTENTS

PREFACE, ⅲ
Chapter 2 State Vectors and Operator Algebra
2.1 State Vectors and Hilbert Space 1
2.1.1 State Vectors and Eigenvectors 1
Examples
2.1.2 Observables and Hermitian Operators 7
Example & Problem
2.1.3 Types of Operators 13
Examples & Problem
★ The Concept of a Basis and Its Role in Hilbert Space 25
2.1.4 Eigenvalue Problem 28
Examples
★ Geometric Meaning of the Eigenvalue Problem 37
2.1.5 Algebraic Method and Ladder Operators 39
Examples
2.1.6 Change of Basis 52
Examples & Problem
★ Taylor Expansion of the Time Evolution Operator and
Dynamical Phase 70
Problem & Solutions