Preface -- Author biography -- 1. The failure of classical physics and the advent of quantum mechanics -- 1.1. A challenge for classical physics -- 1.2. The photoelectric effect -- 1.3. The Compton effect -- 1.4. Heisenberg's uncertainty principle -- 1.5. The correspondence principle -- 1.6. The Schrödinger wave equation -- 1.7. Constraints on solutions -- 1.8. Eigenfunctions and eigenvalues -- 1.9. The principle of superposition -- 1.10. Complementarity -- 1.11. Schrödinger's amplitude equation -- 1.12. The orthonormal set of functions -- 1.13. The equation of continuity -- 1.14. Complete sets of functions -- 1.15. The quantum theory of measurement -- 1.16. Observables and expectation values -- 1.17. Phases and relative phases -- 1.18. Postulates of quantum mechanics -- 1.19. The Schrödinger wave equation under space reflection, space inversion and time reversal -- 1.20. Concluding remarks2. A particle in a one-dimensional box -- 2.1. Introduction -- 2.2. The solution of Schrödinger's amplitude equation -- 2.3. Zero-point energy -- 2.4. The normalisation constant -- 2.5. The parity of eigenfunctions3. Free particles -- 3.1. Introduction -- 3.2. Free particles -- 3.3. Normalisation of stationary wave solutions -- 3.4. Normalisation of progressive wave solutions -- 3.5. Dirac's delta function -- 3.6. Continuous distribution of eigenvalues and Dirac's delta function -- 3.7. Eigenfunctions and eigenvalues of the position operator -- 3.8. Eigenfunctions and eigenvalues of the momentum operator -- 3.9. Normalisation of a free particle eigenfunction using a delta function4. Linear harmonic oscillator -- 4.1. Classical theory -- 4.2. Quantum theory -- 4.3. The asymptotic solution -- 4.4. The general solution -- 4.5. A physically acceptable solution -- 4.6. Energy eigenvalues -- 4.7. Hermite polynomials -- 4.8. The normalisation process -- 4.9. Probability distributions -- 4.10. The importance of the harmonic oscillator -- 4.11. Parity5. The role of Hermitian operators -- 5.1. Linear operators -- 5.2. Hermitian operators -- 5.3. The closure relation -- 5.4. Constants of motion -- 5.5. The classical limit of quantum mechanics : the Ehrenfest theorem -- 5.6. The virial theorem -- 5.7. Heisenberg's uncertainty principle -- 5.8. The parity operator -- 5.9. Antilinear operators -- 5.10. Antiunitary operators6. Potentials with finite discontinuities -- 6.1. Potential steps -- 6.2. The potential barrier -- 6.3. [alpha]-particle decay -- 6.4. The square-well potential7. Spherically symmetric potentials -- 7.1. Introduction -- 7.2. Spherically symmetric potentials -- 7.3. Separation of variables -- 7.4. Solution of the differential equation for F([phi]) -- 7.5. Solution of the differential equation for P([theta]) -- 7.6. Legendre polynomials and associated Legendre functions -- 7.7. Spherical harmonics -- 7.8. Hydrogen and hydrogenic atoms -- 7.9. The solution of the radial equation -- 7.10. Physically acceptable solutions for the radial equation and discrete energy values -- 7.11. The parity of a particle in a spherically symmetric potential -- 7.12. Comparison of the spectral series of hydrogen atom with experiments -- 7.13. The radial wave function -- 7.14. The spectroscopic notation -- 7.15. The normalised solution for the hydrogenic atom -- 7.16. Stationary states8. Matrix mechanics -- 8.1. Matrix representation of an operator -- 8.2. Change of basis and unitary transformation -- 8.3. Coordinate and momentum representations -- 8.4. Continuous distribution of eigenvalues9. Angular momentum -- 9.1. Angular momentum operator -- 9.2. Commutators of various components of L -- 9.3. Commutator of L2 and Lz -- 9.4. Components of the orbital angular momentum operator in spherical polar coordinates -- 9.5. L2 in spherical polar coordinates -- 9.6. Eigenfunctions and eigenvalues of Lz -- 9.7. Eigenvalues of Lz and L2 corresponding to their simultaneous eigenfunctions and ladder operators -- 9.8. Normal Zeeman effect -- 9.9. General theory of angular momentum -- 9.10. Characteristics of ladder operators -- 9.11. Electron spin -- 9.12. Matrix representations of Sx, Sy, Sz -- 9.13. Eigenvectors of Sz -- 9.14. The wave function for the electron -- 9.15. Spins of elementary particles -- 9.16. The average value of spin -- 9.17. Spin and statistics -- 9.18. Addition of angular momenta -- 9.19. Clebsch-Gordan coefficients10. Perturbation theory -- 10.1. Introduction -- 10.2. Time-independent perturbation theory for nondegenerate states -- 10.3. First-order correction to energy -- 10.4. The anomalous Zeeman effect -- 10.5. The first-order correction to the eigenfunction -- 10.6. Second-order non-degenerate perturbation -- 10.7. The second-order correction to energy -- 10.8. The second-order correction to the eigenfunction -- 10.9. First-order perturbation : energy correction in a two-fold degenerate case -- 10.10. The application of perturbation theory to the Stark effect -- 10.11. Time-dependent perturbation theory -- 10.12. Harmonic perturbation -- 10.13. Fermi's golden rule11. Theory of elastic scattering -- 11.1. Introduction -- 11.2. Centre-of-mass and laboratory frames of reference -- 11.3. The effect of collision on the velocity of the centre-of-mass in the laboratory frame -- 11.4. Relation between scattering angles in the laboratory and centre-of-mass frames -- 11.5. Relation between differential cross sections in the laboratory and centre-of-mass frames -- 11.6. Scattering by a stationary target -- 11.7. Relation between the scattering amplitude and differential cross section -- 11.8. Computation of the scattering amplitude -- 11.9. The Born approximation -- 11.10. Scattering of high energy electrons by a screened Coulomb potential -- 11.11. Partial wave analysis -- 11.12. The incident particle wave in terms of partial waves -- 11.13. Phase shift and scattering -- 11.14. A general solution in terms of partial waves -- 11.15. Optical theorem -- 11.16. Scattering by a hard sphere -- 11.17. Scattering from a potential square well -- 11.18. s-wave scattering for a square-well potential -- 11.19. Resonance scattering -- 11.20. Zero-energy scattering and the scattering length -- 11.21. Identical particles12. Dirac's formalism -- 12.1. Introduction -- 12.2. Unitary operators -- 12.3. Unitary transformation -- 12.4. A particular unitary operator -- 12.5 Representations and change of basis -- 12.6. A one-dimensional oscillator -- 12.7. The relation between state vectors and wave functions -- 12.8. A free particle.