Quantum Mechanics: A Conceptual Approach

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 Schrödinger Equation of a Free Particle.

IV The Interpretation of the Wave Function.

V Wave Packets.

VI Concluding Remarks.

VII Problems.

5. The Schrödinger 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 Schrödinger 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 Hückel Molecular Orbital Method.

IX Problems.

Index.