Introduction and orientation 

1  (1) 


1  (2) 


3  (1) 

The photoelectric and Compton effects 


4  (1) 


5  (1) 


6  (2) 


8  (1) 

The foundations of quantum mechanics 


9  (34) 

Operators in quantum mechanics 


9  (10) 


10  (1) 

Eigenfunctions and eigenvalues 


10  (2) 


12  (1) 

Commutation and noncommutation 


13  (1) 

The construction of operators 


14  (1) 


15  (1) 


16  (1) 


17  (2) 

The postulates of quantum mechanics 


19  (6) 


19  (1) 

The fundamental prescription 


20  (1) 

The outcome of measurements 


20  (2) 

The interpretation of the wavefunction 


22  (1) 

The equation for the wavefunction 


23  (1) 

The separation of the Schrodinger equation 


23  (2) 

The specification and evolution of states 


25  (7) 


25  (2) 

The uncertainty principle 


27  (2) 

Consequences of the uncertainty principle 


29  (1) 

The uncertainty in energy and time 


30  (1) 

Timeevolution and conservation laws 


30  (2) 

Matrices in quantum mechanics 


32  (4) 


32  (2) 

The diagonalization of the hamiltonian 


34  (2) 

The plausibility of the Schrodinger equation 


36  (7) 


36  (2) 

The propagation of particles 


38  (1) 

The transition to quantum mechanics 


39  (1) 


40  (3) 

Linear motion and the harmonic oscillator 


43  (28) 

The characteristics of acceptable wavefunctions 


43  (1) 

Some general remarks on the Schrodinger equation 


44  (3) 

The curvature of the wavefunction 


45  (1) 


45  (1) 

The emergence of quantization 


46  (1) 

Penetration into nonclassical regions 


46  (1) 


47  (4) 


48  (1) 

The significance of the coefficients 


48  (1) 


49  (1) 


50  (1) 

Penetration into and through barriers 


51  (4) 

An infinitely thick potential wall 


51  (1) 

A barrier of finite width 


52  (2) 

The Eckart potential barrier 


54  (1) 


55  (5) 


56  (1) 

Features of the solutions 


57  (1) 

The twodimensional square well 


58  (1) 


59  (1) 


60  (6) 


61  (2) 

Properties of the solutions 


63  (2) 


65  (1) 

Translation revisited: The scattering matrix 


66  (5) 


68  (3) 

Rotational motion and the hydrogen atom 


71  (27) 


71  (5) 

The hamiltonian and the Schrodinger equation 


71  (2) 


73  (1) 

The shapes of the wavefunctions 


74  (2) 


76  (1) 


76  (8) 

The Schrodinger equation and its solution 


76  (3) 

The angular momentum of the particle 


79  (2) 

Properties of the solutions 


81  (1) 


82  (2) 

Motion in a Coulombic field 


84  (14) 

The Schrodinger equation for hydrogenic atoms 


84  (1) 

The separation of the relative coordinates 


85  (1) 

The radial Schrodinger equation 


85  (5) 

Probabilities and the radial distribution function 


90  (1) 


91  (3) 

The degeneracy of hydrogenic atoms 


94  (2) 


96  (2) 


98  (24) 

The angular momentum operators 


98  (4) 

The operators and their commutation relations 


99  (2) 

Angular momentum observables 


101  (1) 


101  (1) 

The definition of the states 


102  (10) 

The effect of the shift operators 


102  (2) 

The eigenvalues of the angular momentum 


104  (2) 

The matrix elements of the angular momentum 


106  (2) 

The angular momentum eigenfunctions 


108  (2) 


110  (2) 

The angular momenta of composite systems 


112  (10) 

The specification of coupled states 


112  (1) 

The permitted values of the total angular momentum 


113  (2) 

The vector model of coupled angular momenta 


115  (2) 

The relation between schemes 


117  (2) 

The coupling of several angular momenta 


119  (1) 


120  (2) 


122  (46) 

The symmetries of objects 


122  (7) 

Symmetry operations and elements 


123  (1) 

The classification of molecules 


124  (5) 


129  (16) 

The definition of a group 


129  (1) 

Group multiplication tables 


130  (1) 


131  (4) 

The properties of matrix representations 


135  (2) 

The characters of representations 


137  (1) 


138  (1) 

Irreducible representations 


139  (3) 

The great and little orthogonality theorems 


142  (3) 


145  (6) 

The reduction of representations 


146  (1) 


147  (4) 

The symmetry properties of functions 


151  (10) 

The transformation of porbitals 


151  (1) 

The decomposition of directproduct bases 


152  (3) 


155  (2) 


157  (2) 


159  (2) 


161  (4) 

The generators of rotations 


161  (1) 

The representation of the full rotation group 


162  (2) 


164  (1) 


165  (3) 


166  (2) 

Techniques of approximation 


168  (39) 

Timeindependent perturbation theory 


168  (15) 

Perturbation of a twolevel system 


169  (2) 


171  (1) 

The firstorder correction to the energy 


172  (2) 

The firstorder correction to the wavefunction 


174  (1) 

The secondorder correction to the energy 


175  (1) 

Comments on the perturbation expressions 


176  (2) 

The closure approximation 


178  (2) 

Perturbation theory for degenerate states 


180  (3) 


183  (4) 


183  (2) 


185  (2) 

The HellmannFeynman theorem 


187  (2) 

Timedependent perturbation theory 


189  (18) 

The timedependent behaviour of a twolevel system 


189  (3) 


192  (1) 

Manylevel systems: the variation of constants 


193  (2) 

The effect of a slowly switched constant perturbation 


195  (2) 

The effect of an oscillating perturbation 


197  (2) 

Transition rates to continuum states 


199  (1) 

The Einstein transition probabilities 


200  (3) 

Lifetime and energy uncertainty 


203  (1) 


204  (3) 

Atomic spectra and atomic structure 


207  (42) 

The spectrum of atomic hydrogen 


207  (12) 

The energies of the transitions 


208  (1) 


209  (3) 

Orbital and spin magnetic moments 


212  (2) 


214  (2) 

The finestructure of spectra 


216  (1) 

Term symbols and spectral details 


217  (1) 

The detailed spectrum of hydrogen 


218  (1) 


219  (10) 


219  (3) 


222  (2) 


224  (1) 


225  (4) 


229  (13) 

Penetration and shielding 


229  (2) 


231  (2) 


233  (1) 


234  (2) 

Term symbols and transitions of manyelectron atoms 


236  (3) 

Hund's rules and the relative energies of terms 


239  (1) 

Alternative coupling schemes 


240  (2) 


242  (7) 


242  (1) 

The anomalous Zeeman effect 


243  (2) 


245  (1) 


246  (3) 

An introduction to molecular structure 


249  (38) 

The BornOppenheimer approximation 


249  (4) 

The formulation of the approximation 


250  (1) 

An application: the hydrogen moleculeion 


251  (2) 


253  (13) 

Linear combinations of atomic orbitals 


253  (5) 


258  (1) 

Configuration interaction 


259  (2) 


261  (4) 

Heteronuclear diatomic molecules 


265  (1) 

Molecular orbital theory of polyatomic molecules 


266  (12) 

Symmetryadapted linear combinations 


266  (3) 


269  (5) 


274  (2) 

Further aspects of ligand field theory 


276  (2) 

The band theory of solids 


278  (9) 

The tightbinding approximation 


279  (2) 


281  (3) 


284  (1) 


285  (2) 

The calculation of electronic structure 


287  (55) 

The HartreeFock selfconsistent field method 


288  (14) 

The formulation of the approach 


288  (1) 

The HartreeFock approach 


289  (2) 

Restricted and unrestricted HartreeFock calculations 


291  (2) 


293  (3) 

The selection of basis sets 


296  (5) 

Calculational accuracy and the basis set 


301  (1) 


302  (14) 

Configuration state functions 


303  (1) 

Configuration interaction 


303  (2) 


305  (3) 

Multiconfiguration and multireference methods 


308  (2) 

MollerPlesset manybody perturbation theory 


310  (3) 

The coupledcluster method 


313  (3) 

Density functional theory 


316  (5) 

KohnSham orbitals and equations 


317  (2) 

Exchangecorrelation functionals 


319  (2) 

Gradient methods and molecular properties 


321  (4) 

Energy derivatives and the Hessian matrix 


321  (1) 

Analytical derivatives and the coupled perturbed equations 


322  (3) 


325  (7) 

Conjugated πelectron systems 


326  (3) 

Neglect of differential overlap 


329  (3) 


332  (4) 


333  (1) 

Quantum mechanicsmolecular mechanics 


334  (2) 

Software packages for electronic structure calculations 


336  (6) 


339  (3) 

Molecular rotations and vibrations 


342  (40) 

Spectroscopic transitions 


342  (2) 


342  (2) 


344  (1) 


344  (13) 


345  (4) 


349  (1) 

Pure rotational selection rules 


349  (2) 

Rotational Raman selection rules 


351  (2) 


353  (4) 

The vibrations of diatomic molecules 


357  (8) 

The vibrational energy levels of diatomic molecules 


357  (2) 


359  (1) 

Vibrational selection rules 


360  (2) 

Vibrationrotation spectra of diatomic molecules 


362  (2) 

Vibrational Raman transitions of diatomic molecules 


364  (1) 

The vibrations of polyatomic molecules 


365  (14) 


365  (3) 

Vibrational selection rules for polyatomic molecules 


368  (1) 

Group theory and molecular vibrations 


369  (4) 

The effects of anharmonicity 


373  (3) 


376  (1) 


377  (2) 

Appendix 10.1 Centrifugal distortion 


379  (3) 


380  (2) 

Molecular electronic transitions 


382  (25) 

The states of diatomic molecules 


382  (4) 


382  (2) 

Decoupling and Adoubling 


384  (2) 


386  (1) 


386  (4) 

The FranckCondon principle 


386  (3) 

The rotational structure of vibronic transitions 


389  (1) 

The electronic spectra of polyatomic molecules 


390  (6) 


391  (1) 


391  (2) 

Vibronically allowed transitions 


393  (2) 

Singlettriplet transitions 


395  (1) 

The fate of excited species 


396  (11) 


396  (1) 


397  (2) 

The conservation of orbital symmetry 


399  (1) 


399  (2) 


401  (2) 

Photochemically induced electrocyclic reactions 


403  (1) 

Photochemically induced cycloaddition reactions 


404  (2) 


406  (1) 

The electric properties of molecules 


407  (29) 

The response to electric fields 


407  (11) 

Molecular response parameters 


407  (2) 

The static electric polarizability 


409  (2) 

Polarizability and molecular properties 


411  (2) 

Polarizabilities and molecular spectroscopy 


413  (1) 

Polarizabilities and dispersion forces 


414  (4) 


418  (1) 

Bulk electrical properties 


418  (9) 

The relative permittivity and the electric susceptibility 


418  (2) 


420  (2) 


422  (5) 


427  (9) 

Circular birefringence and optical rotation 


427  (2) 

Magnetically induced polarization 


429  (2) 


431  (3) 


434  (2) 

The magnetic properties of molecules 


436  (37) 

The descriptions of magnetic fields 


436  (6) 

The magnetic susceptibility 


436  (1) 


437  (2) 


439  (1) 

Derivatives of vector functions 


440  (1) 


441  (1) 


442  (10) 

The perturbation hamiltonian 


442  (2) 

The magnetic susceptibility 


444  (3) 


447  (3) 

The diamagnetic current density 


450  (1) 

The paramagnetic current density 


451  (1) 

Magnetic resonance parameters 


452  (21) 


452  (4) 

The diamagnetic contribution to shielding 


456  (2) 

The paramagnetic contribution to shielding 


458  (1) 


459  (3) 


462  (1) 


463  (4) 

Nuclear spinspin coupling 


467  (4) 


471  (2) 


473  (40) 

The formulation of scattering events 


473  (6) 

The scattering crosssection 


473  (2) 

Stationary scattering states 


475  (4) 

Partialwave stationary scattering states 


479  (18) 


479  (1) 

The partialwave equation 


480  (1) 

Freeparticle radial wavefunctions and the scattering phase shift 


481  (3) 

The JWKB approximation and phase shifts 


484  (2) 

Phase shifts and the scattering matrix element 


486  (2) 

Phase shifts and scattering crosssections 


488  (2) 

Scattering by a spherical square well 


490  (2) 

Background and resonance phase shifts 


492  (2) 


494  (1) 

Resonance contributions to the scattering matrix element 


495  (2) 


497  (5) 


497  (1) 

Multichannel stationary scattering states 


498  (1) 


498  (3) 

The S matrix and multichannel resonances 


501  (1) 


502  (6) 

The integral scattering equation and Green's functions 


502  (2) 


504  (4) 

Appendix 14.1 The derivation of the BreitWigner formula 


508  (1) 

Appendix 14.2 The rate constant for reactive scattering 


509  (4) 


510  (3) 


513  (40) 


513  (6) 


513  (2) 


515  (1) 


516  (2) 


518  (1) 

Solutions of the Schrodinger equation 


519  (15) 

The motion of wavepackets 


519  (2) 

The harmonic oscillator: solution by factorization 


521  (2) 

The harmonic oscillator: the standard solution 


523  (2) 


525  (1) 


526  (1) 


527  (1) 

The HartreeFock equations 


528  (4) 


532  (1) 

The unitarity of the S matrix 


533  (1) 

Group theory and angular momentum 


534  (3) 

The orthogonality of basis functions 


534  (1) 

Vector coupling coefficients 


535  (2) 


537  (6) 

Electric dipole transitions 


537  (1) 


538  (2) 


540  (1) 


541  (2) 

The electromagnetic field 


543  (4) 


543  (3) 

The dipolar vector potential 


546  (1) 


547  (6) 


547  (2) 


549  (4) 


553  (4) 
Appendix 1 

557  (5) 
Appendix 2 

562  (1) 
Answers to selected problems 

563  (2) 
Index 

565  