Quantum Mechanics: Theory and Applications

I: Mathematical Preliminaries.- 1: The Dirac Delta Function.- 2: Fourier Transforms.- II: Basic Quantum Mechanics.- 3: Particles and Waves and the Uncertainty Principle.- 4: Time Dependent Schrödinger Equation.- 5: Propagation of Wave Packets and Concept of Group Velocity.- 6: Bound State Solutions of the Schrödinger Equation.- 7: Linear Harmonic Oscillator: I Solution of the Schrödinger Equation and Relationship with the Classical Oscillator.- 8: One-Dimensional Barrier Transmission Problems.- 9: Angular Momentum I The Spherical Harmonics.- 10: Spherically Symmetric Potentials Hydrogen Atom Problem, Rotation Vibration Spectra, Three-Dimensional Oscillator.- 11: Dirac’s Bra and Ket Algebra.- 12: Linear Harmonic Oscillator II Solutions Using Bra and Ket Algebra.- 13: Angular Momentum II Using Bra and Ket Algebra.- 14: Experiments with Spin Half Particles The Stern-Gerlach Experiment, Larmor Precession and Magnetic Resonance.- 15: Angular momentum III Eigenfunctions Using Operator Algebra.- 16: The Double Well Potential and the Krönig-Penney Model.- 17: The JWKB Approximation.- 18: Addition of Angular Momenta: The Clebsch-Gordan Coefficients.- 19: Time Independent Perturbation Theory.- 20: Effects of Magnetic Field.- 21: The Variational Method.- 22: The Helium Atom and the Exclusion Principle.- 23: Some Select Topics.- 24: Elementary Theory of Scattering.- 25: Time Dependent Perturbation Theory.- 26: The Semi-Classical Theory of Radiation and the Einstein Coefficients.- 27: The Quantum Theory of Radiation and Its Interaction with Matter.- 28: Relativistic Theory.- Appendices.