Quantum Physics States, Observables and Their Time Evolution

Preface
Contents
1 Quantum Harmonic Oscillator
	1.1 The Gate to Quantum Mechanics
	1.2 Derivation of Energy Values and Transition Matrix Elements of the Quantum Harmonic Oscillator
		1.2.1 From the Classical to the Quantum Oscillator
		1.2.2 Finding the Mathematical Properties of the Operators P, Q, and H
	1.3 Pure States, Mixtures and Quantum Mechanical Probabilities and Transition Rates
		1.3.1 Introduction
		1.3.2 Energy-Loss (Franck-Hertz) Experiments
		1.3.3 The State of the Ensemble of CO Molecules Participating in the Energy-Loss Experiment
		1.3.4 Interpretation of the Experimental Results
	1.4 Fundamental Postulates of Quantum Mechanics
		1.4.1 Algebra of Observables—Fundamental Postulate I
		1.4.2 Quantum Mechanical States—Fundamental Postulate II
		1.4.3 Pure State—Fundamental Postulate IIa
		1.4.4 Uncertainties and Standard Deviations
		1.4.5 Heisenberg Uncertainty Principle
	1.5 Radiative Transitions
		1.5.1 Dipole Radiation
		1.5.2 Einstein Coefficients
		1.5.3 Comparison with Experimental Results
	1.6 Summary
	Problems
		For Sect.1.2
		For Sect.1.3
		For Sect.1.4
		For Sect.1.5
2 Angular Momentum
	2.1 Introduction
	2.2 Introduction to Angular Momentum
		2.2.1 Rigid Dumbbell as a Model of a Rotating Diatomic Molecule
	2.3 Angular Momentum: Algebraic Solutions
	2.4 Observables of the Rotating Diatomic Molecule
		2.4.1 The Algebra E(E(3)) of Observables of the Rotating Dumbbell
		2.4.2 Basic Observables—Fundamental Postulate III
		2.4.3  Absorption Spectrum for Diatomic Molecules
		2.4.4  Absorption Spectrum for Non-rigid Diatomic Molecules
	2.5 Angular Momentum States and Calculation of Probabilities
	2.6 Relationship Between SU(2) and SO(3)
	2.7 Summary
	Problems
		For Sect.2.2
		For Sect.2.3
		For Sect.2.4
		For Sect.2.5
3 Combinations of Quantum Physical Systems
	3.1 Introduction
	3.2 Separation of a Hamiltonian
		3.2.1 Introduction
		3.2.2 A Non-interacting Particle in Three-Dimensional Space Viewed as Three Non-interacting Particles, Each Moving in a One-Dimensional Space
		3.2.3 Two Interacting Particles: Center-of-Mass Motion andRelative Motion
	3.3 Combination of Quantum Physical Systems
		3.3.1 Mathematical Preliminaries
		3.3.2 Basic Postulate for the Combination of Quantum Systems
		3.3.3 Combination of Quantum Systems: Direct-Product Spaces—Fundamental Postulate IV
		3.3.4 Complete Sets of Commuting Observables
		3.3.5 The Rotating Dumbbell
	3.4 The Vibrating Rotator
		3.4.1 The Interplay of Rotations and Vibrations
	3.5 Addition of Two Angular Momenta: Clebsch-Gordan Coefficients
	3.6 Tensor Operators and the Wigner-Eckart Theorem
		3.6.1 Mathematical Note
	3.7 Summary
	Problems
		For Sect. 3.2
		For Sect. 3.3
		For Sect. 3.4
		For Sect. 3.5
		For Sect. 3.6
4 Stationary Perturbation Theory
	4.1 Stationary Perturbation Theory and Its Underlying Assumptions
		4.1.1 Introduction
		4.1.2 Magnetic Moment in a Magnetic Field
		4.1.3 Quantum Rotator in a Uniform Magnetic Field
		4.1.4 Perturbation Theory
	4.2 Stationary Perturbation Expansion
	4.3 Degenerate, Stationary Perturbation Expansion
		4.3.1 The Stark Effect
	4.4 Summary
	Problems
		For Sect.4.1.1
		For Sect.4.2
		For Sect.4.3
5 Time Evolution of Quantum Systems
	5.1 Time Evolution
		5.1.1 Introduction
	5.2 Time Evolution of States, Observables and Probabilities
	5.3 Time Evolution in Standard Quantum Mechanics
		5.3.1 Time Development in the Schrödinger Picture—Fundamental Postulate Va
		5.3.2 Time Development in the Heisenberg Picture—Fundamental Postulate Vb
	5.4 Time-Dependent Hamiltonian
		5.4.1 Time Development in the Heisenberg Picture—Fundamental Postulate VIb
	5.5 Precession of a Spinning Particle in a Magnetic Field: The Interpretation of the Schrödinger and Heisenberg Pictures
		5.5.1 Precession of a Classical Spinning Particle in a Magnetic Field
		5.5.2 Mathematical Preliminaries: Rotation of Operators and States
		5.5.3 Precession of a Spinning Particle in a Magnetic Field: The Schrödinger Picture
		5.5.4 Precession of a Spinning Particle in a Magnetic Field: The Heisenberg Picture
	5.6 Magnetic Resonance
		5.6.1 Hamiltonian for Magnetic Resonance
		5.6.2 Magnetic Resonance in the Schrödinger Picture
		5.6.3 Magnetic Resonance Experiments
	5.7 Gibbs Distribution
	5.8 Summary
	Problems
		For Sect.5.3
		For Sect.5.4
		For Sect.5.5
		For Sect.5.6
		For Sect.5.7
Epilogue
Appendix: Mathematical Preliminaries
	A.1 Introduction
	A.2 Linear, Scalar-Product Spaces
	A.3 Linear Operators
	A.4 Basis Systems and Eigenvector Decompositions
		A.4.1 Discrete Basis Vectors in Real, Three-Dimensional Space
		A.4.2 Discrete Basis Vectors in Infinite-Dimensional, Complex Space
		A.4.3 Continuous Basis Systems of a Linear Space
		A.4.4 Working with Eigenvectors and Basis Vector Expansions
	A.5 Realizations by Matrices and Functions
	A.6 Summary
	Problems
		For Sect. A.2
		For Sect. A.3
		For Sect. A.4
		For Sect. A.5
Index