Quantum mechanics: a conceptual approach

Abstract

Preface. 1. The Discovery of Quantum Mechanics. I Introduction. II Planck and Quantization. III Bohr and the Hydrogen Atom. IV Matrix Mechanics. V The Uncertainty Relations. VI Wave Mechanics. VII The Final Touches of Quantum Mechanics. VIII Concluding Remarks. 2. The Mathematics of Quantum Mechanics. I Introduction. II Differential Equations. III Kummer's Function. IV Matrices. V Permutations. VI Determinants. VII Properties of Determinants. VIII Linear Equations and Eigenvalues. IX Problems. 3. Classical Mechanics. I Introduction. II Vectors and Vector Fields. III Hamiltonian Mechanics. IV The Classical Harmonic Oscillator. V Angular Momentum. VI Polar Coordinates. VII Problems. 4. Wave Mechanics of a Free Particle. I Introduction. II The Mathematics of Plane Waves. III The Schrodinger Equation of a Free Particle. IV The Interpretation of the Wave Function. V Wave Packets. VI Concluding Remarks. VII Problems. 5. The Schrodinger Equation. I Introduction. II Operators. III The Particle in a Box. IV Concluding Remarks. V Problems. 6. Applications. I Introduction. II A Particle in a Finite Box. III Tunneling. IV The Harmonic Oscillator. V Problems. 7. Angular Momentum. I Introduction. II Commuting Operators. III Commutation Relations of the Angular Momentum. IV The Rigid Rotor. V Eigenfunctions of the Angular Momentum. VI Concluding Remarks. VII Problems. 8. The Hydrogen Atom. I Introduction. II Solving the Schrodinger Equation. III Deriving the Energy Eigenvalues. IV The Behavior of the Eigenfunctions. V Problems. 9. Approximate Methods. I Introduction. II The Variational Principle. III Applications of the Variational Principle. IV Perturbation Theory for a Nondegenerate State. V The Stark Effect of the Hydrogen Atom. VI Perturbation Theory for Degenerate States. VII Concluding Remarks. VIII Problems. 10. The Helium Atom. I Introduction. II Experimental Developments. III Pauli's Exclusion Principle. IV The Discovery of the Electron Spin. V The Mathematical Description of the Electron Spin. VI The Exclusion Principle Revisited. VII Two--Electron Systems. VIII The Helium Atom. IX The Helium Atom Orbitals. X Concluding Remarks. XI Problems. 11 Atomic Structure. I Introduction. II Atomic and Molecular Wave Function. III The Hartree--Fock Method. IV Slater Orbitals. V Multiplet Theory. VI Concluding Remarks. VII Problems. 12 Molecular Structure. I Introduction. II The Born--Oppenheimer Approximation. III Nuclear Motion of Diatomic Molecules. IV The Hydrogen Molecular Ion. V The Hydrogen Molecule. VI The Chemical Bond. VII The Structures of Some Simple Polyatomic Molecules. VIII The Huckel Molecular Orbital Method. IX Problems. Index.