Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 The wave function -- 1.1 Wave motion -- Plane wave -- Composite wave -- Addition of two plane waves -- 1.2 Wave packet -- Gaussian wave number distribution -- Square pulse wave number distribution -- Uncertainty relation -- 1.3 Dispersion of a wave packet -- Gaussian wave packet -- 1.4 Particles and waves -- 1.5 Heisenberg uncertainty principle -- 1.6 Young's double-slit experiment -- 1.7 Stern-Gerlach experiment -- 1.8 Physical interpretation of the wave function -- Problems -- 2 Schrödinger wave mechanics -- 2.1 The Schrödinger equation -- 2.2 The wave function -- Interpretation -- Normalization -- Momentum-space wave function -- 2.3 Expectation values of dynamical quantities -- Ehrenfest's theorems -- Heisenberg uncertainty principle -- 2.4 Time-independent Schrödinger equation -- 2.5 Particle in a one-dimensional box -- 2.6 Tunneling -- 2.7 Particles in three dimensions -- Multi-particle system -- 2.8 Particle in a three-dimensional box -- Degeneracy of energy levels -- Problems -- 3 General principles of quantum theory -- 3.1 Linear operators -- 3.2 Eigenfunctions and eigenvalues -- Scalar product and orthogonality -- 3.3 Hermitian operators -- Eigenvalues -- Orthogonality theorem -- Extended orthogonality theorem -- 3.4 Eigenfunction expansions -- Completeness -- 3.5 Simultaneous eigenfunctions -- 3.6 Hilbert space and Dirac notation -- Bra vectors -- Projection operator -- 3.7 Postulates of quantum mechanics -- State function -- Physical quantities or observables -- Measurement of observable properties -- Collapse of the state function -- Time evolution of the state function -- 3.8 Parity operator -- 3.9 Hellmann-Feynman theorem -- 3.10 Time dependence of the expectation value -- 3.11 Heisenberg uncertainty principle -- Position-momentum uncertainty principle.

Minimum uncertainty wave packet -- Energy-time uncertainty principle -- Problems -- 4 Harmonic oscillator -- 4.1 Classical treatment -- 4.2 Quantum treatment -- Ladder operators -- Quantization of the energy -- Non-degeneracy of the energy levels -- 4.3 Eigenfunctions -- Lowering and raising operations -- Excited-state eigenfunctions -- Eigenfunctions in terms of Hermite polynomials -- Physical interpretation -- 4.4 Matrix elements -- 4.5 Heisenberg uncertainty relation -- 4.6 Three-dimensional harmonic oscillator -- Problems -- 5 Angular momentum -- 5.1 Orbital angular momentum -- Commutation relations -- 5.2 Generalized angular momentum -- Ladder operators -- Determination of the eigenvalues -- 5.3 Application to orbital angular momentum -- Ladder operators -- Normalization of… -- Spherical harmonics -- Relationship of spherical harmonics to associated Legendre polynomials -- 5.4 The rigid rotor -- 5.5 Magnetic moment -- Interaction with a magnetic field -- Problems -- 6 The hydrogen atom -- 6.1 Two-particle problem -- 6.2 The hydrogen-like atom -- 6.3 The radial equation -- Ladder operators -- Orthonormal properties of… -- Evaluation of the constants… -- Quantization of the energy -- Determination of the eigenfunctions -- Radial functions in terms of associated Laguerre polynomials -- Solution for positive energies -- Infinite nuclear mass -- 6.4 Atomic orbitals -- s orbitals -- p orbitals -- d orbitals -- Radial functions and expectation values -- 6.5 Spectra -- Pseudo-Zeeman effect -- Problems -- 7 Spin -- 7.1 Electron spin -- 7.2 Spin angular momentum -- 7.3 Spin one-half -- Pauli spin matrices -- 7.4 Spin-orbit interaction -- Problems -- 8 Systems of identical particles -- 8.1 Permutations of identical particles -- Two-particle systems -- Three-particle systems -- N-particle systems -- 8.2 Bosons and fermions -- 8.3 Completeness relation.

8.4 Non-interacting particles -- Probability densities -- Electron spin and the helium atom -- 8.5 The free-electron gas -- 8.6 Bose-Einstein condensation -- Problems -- 9 Approximation methods -- 9.1 Variation method -- Variation theorem -- Ground-state eigenfunction -- Example: particle in a box -- Example: harmonic oscillator -- Excited-state energies -- 9.2 Linear variation functions -- 9.3 Non-degenerate perturbation theory -- First-order corrections -- Second-order corrections -- Summary -- Relation to variation method -- 9.4 Perturbed harmonic oscillator -- 9.5 Degenerate perturbation theory -- 'Correct' zero-order eigenfunctions -- First-order corrections to the eigenfunctions -- Example: hydrogen atom in an electric field -- 9.6 Ground state of the helium atom -- Perturbation theory treatment -- Variation method treatment -- Problems -- 10 Molecular structure -- 10.1 Nuclear structure and motion -- Born-Oppenheimer approximation -- Born-Huang treatment -- 10.2 Nuclear motion in diatomic molecules -- Center-of-mass coordinates -- Electronic motion and the nuclear potential function -- Nuclear motion -- Higher-order approximation for nuclear motion -- Problems -- Appendix A Mathematical formulas -- Useful power series expansions -- Binomial expansions -- Useful integrals -- Integration by parts -- Gamma function -- Trigonometric functions -- Hyperbolic functions -- Schwarz's inequality -- Vector relations -- Spherical coordinates (r, Theta, Phi) -- Plane polar coordinates (r, Phi) -- Appendix B Fourier series and Fourier integral -- Fourier series -- Other variables -- Complex form -- Parseval's theorem -- Fourier integral -- Fourier integral in three dimensions -- Parseval's theorem -- Appendix C Dirac delta function -- Appendix D Hermite polynomials -- Recurrence relations -- Differential equation -- Integral relations -- Completeness.

Appendix E Legendre and associated Legendre polynomials -- Legendre polynomials -- Recurrence relations -- Differential equation -- Rodrigues' formula -- Associated Legendre polynomials -- Differential equation -- Orthogonality -- Normalization -- Completeness -- Appendix F Laguerre and associated Laguerre polynomials -- Laguerre polynomials -- Differential equation -- Associated Laguerre polynomials -- Differential equation -- Integral relations -- Completeness -- Appendix G Series solutions of differential equations -- General procedure -- Applications -- Harmonic oscillator -- Orbital angular momentum -- Radial equation for the hydrogen-like atom -- Appendix H Recurrence relation for hydrogen-atom expectation values -- Appendix I Matrices -- Matrix algebra -- Square matrices -- Determinants -- Special square matrices -- Linear vector space -- Eigenvalues -- Trace -- Appendix J Evaluation of the two-electron interaction integral -- Selected bibliography -- Applied mathematical methods -- Undergraduate physical chemistry -- History and philosophy of quantum theory -- Some 'classic' quantum mechanics texts -- Some recent quantum mechanics texts -- Angular momentum -- Atoms and atomic spectra -- More advanced applications of quantum mechanics -- Compilations of problems in quantum mechanics -- Index.