SEARCH Articles Figures Tables A Further Approximation The AB Equation A Second Approximation in the Inner Region A The Continuum Approximation Accuracy of the KLI Approximation An approximate equation for the singlet density Appendix to chapter 4. The random phase approximation Applications of the simplified approximation formula Approximate Equations of the Adiabatic Theory Approximate Formulations of the Fock Equations Approximate Representation of the Diabatic Electronic Wavefunction Approximate Solutions of the PB Equation Approximate Solutions of the Schrodinger equation Approximate Treatments of the HJ Ground Electronic State Approximate forms of the macroscopic rate coefficient Approximate neglect of pressure variations in the intermediate diffusion range Approximate solution for the structure of a detonation Approximate solution of the Dirac equation Approximate value of the diffusivity Approximating the Schrodinger Equation Approximating the saturated vapor pressure of liquids Approximation by the Use of Difference Equations Approximation for the Valence Energy Approximation of the Convective Transport Terms Approximation of the Diffusive Transport Terms Approximation of the Effectiveness Factor for Bimolecular Reactions Approximation of the process impulse response Approximation of the process transfer function Approximation of the stress-strain curve Approximation to the Energy-Transfer Cross-Section Approximations for the direct correlation function Approximations that further simplify the energy equation Approximations to the Coulomb-Breit matrix elements Approximations to the Many-Electron Wave Function Approximations to the Poisson-Boltzmann Equation Approximations towards the Cooper-Zare model Better Approximate Solutions of the Time-Independent Schrodinger Equation Beyond the Born-Oppenheimer Approximation Beyond the Harmonic Approximation Beyond the Local Density Approximation Beyond the Orbital Approximation Beyond the Single-Configuration Approximation Beyond the adiabatic approximation Box 6-2 The Logic of Approximations Breakdown of the Independent Electron Approximation Breakdown of the Normal Mode Approximation By Yehuda Haas and Shmuel Zilberg The Crude Born-Oppenheimer Adiabatic Approximation of Molecular Potential Energies Capillary Forces Calculated with the Circular Approximation Common Approximations for the Current Distribution Conductivity imaging by the Born approximation Correction of the Crude Adiabatic Approximation Criticism of the Gaussian approximation Demixtion curves and the Flory-Huggins approximation Dependent Tunneling in the Born-Oppenheimer Approximation Developing a long-pipe approximation to the full compressible flow equations Dois Approximate Solution of the Smoluchowski Equation Domain Partition and Linear Approximation of the Yield Function Ellipsoid in the Electrostatics Approximation Energy bands in the free-electron approximation symmorphic space groups Equilibrium between an oxide and oxygen the Wagner prevalent defect approximation Error of the difference approximation Example using the long-pipe approximation Exciton states beyond the Heitler London approximation Expansion and approximation of the Poisson-Boltzmann equation to one non-zero term only Finite difference approximation of the boundary-value problem Harmonic approximation of the potential Helmholtz Free Energy from the CS Approximation High frequency (WKBJ) approximation for the Greens function High frequency approximations in the solution of an acoustic wave equation Horners method for approximating to the real roots of numerical equations How does the Born-Oppenheimer approximation break down Integral approximations of the acoustic wavefield Ion-Solvent Interactions According to the Mean Spherical Approximation Ionic Fluids in the Mean Spherical Approximation Linear approximation of the Local Approximations to the Exact-Decoupling Transformation Main Approximations of the LSW Approach Many-Body Perturbation Theory and the GW Approximation Mechanics of Films The Lubrication Approximation Methods using a series expansion as an approximation for the exponential integral Methods using a simple approximation for the exponential integral Model Hamiltonian in the Kirkwood Approximation Model Hamiltonians in the Macroscopic Approximation Molecules and the Born-Oppenheimer Approximation Moments and the quadrature approximation Nanosphere in the Quasi-Static Approximation Nature of the Approximation Normal modes in the harmonic approximation Perturbation theory. A comparison with results obtained in the Heitler-London approximation Physical grounds for the DFT approximations Polyatomic Systems in Approximation The Cell Model Possible approximations for the weak base Properties in the Matrix Approximations Quantum-mechanical treatment the first Born approximation Quantum-mechanical treatment the second Born approximation Quasi-linear approximation of the modified Greens operator Refinement beyond the simple mean field approximation Reflectivity under the Kinematic Approximation Reorientation in the impact approximation Resolution of the Identity and Local Correlation Approximations Resolution of the identity approximation Scattering atmospheres the two-stream approximation Screening the Thomas-Fermi approximation Semi-classical Expansion and the WKB Approximation Some approximation problems in the Hilbert spaces of geophysical data Some of the worlds most important crop plants and approximate dates for domestication Spherical approximation of the boundary condition Successive approximations of the Symmetry of the One-electron Approximation Hamiltonian Taylor series approximation of the The --electron approximation The AO approximation The Adiabatic and Born-Oppenheimer Approximations The Adiabatic and Harmonic Approximations The Alfrey approximation The Algebraic Approximation The Approximate Method The Atomic-Sphere Approximation (ASA) The Bar-Graph Approximation The Basis Set Approximation The Boltzmann Equation Collision Term Approximation The Bom-Oppenheimer Approximation The Born-Oppenheimer Approximation The Born-Oppenheimer Approximation Potential Energy Surfaces The Born-Oppenheimer Approximation and its Breakdown Nonadiabatic Processes The Carnahan-Starling Approximation The Central Field Approximation (Non-Relativistic) The Continued Fraction Approximations The Current Approximation The Current Approximation Function The Debye approximation The Debye-Huckel Approximation Results The Derjaguin approximation The Einstein approximation The Electronic States of Atoms. III. Higher-Order Approximations The Electrostatics Approximation The Enskog Approximation The Finite Difference Approximation The Fourier Series Approximation The Franck-Condon Approximation The Frozen-Core Approximation The Gaussian approximation The Generalized Gradient Approximation The Group Born-Oppenheimer Approximation The Hard-Rod Approximations The Harmonic Approximation The Hartree Approximation The Hartree-Fock Approximation The Hartree-Fock approximation in jellium The Hellmann-Feynman Theorem for Approximate Wavefunctions The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation The Independent Electron Approximation The Inverse Langevin Approximation The Kirkwood superposition approximation The LiH molecule approximate molecular orbital calculations The Line Tension Approximation The Local Density Approximation The Long-Chain Approximation The MARI Approximation The MO Approximation The MO-LCAO Approximation The Mean-Spherical Equal Arm Stretching Approximation General Formalism The Mean-field Approximation The Method of Successive Approximations The Neglect of Differential Overlap Approximation The No Virtual Pair Approximation The No-Pair Approximation The Non-inertial Approximation The One-Electron Approximation The One-Valley Approximation The Orbital Approximation Helium The Orbital Approximation for Lithium The PCM-CC-PTE Approximation The Pairwise Additive Approximation The Parallel-Series Kinetic Model Approximation The Pauli Approximation The Point-Dipole Approximation The Pool Chemical Approximation The Pseudo-Steady-State Approximation The Quasi Steady State Approximation The Quasi-Equilibrium Approximation Enzymatic Reaction Kinetics The Quasi-Harmonic Approximation The Quasi-equilibrium Approximation The Quest for Approximate Exchange-Correlation Functionals The Rate-Limiting Step (RLS) Approximation The Resonant Wave Approximation The Rigid Rotor Harmonic Oscillator Approximation The SLG approximation The Short-Time Approximation The Singh and Dutt approximation The Steady-State Approximation The Stokes approximation The Thin Film Approximation The Thin Gap Approximation The Thin-Gap Approximation - Films with a Free Surface The Thin-Gap Approximation - Lubrication Problems The Trapezoidal Approximation The Two-Centre Approximation The Valence-Electron Approximation The Variational Approach to Approximations The WKB Approximation The Wavefunctions of Many-Electron Atoms Can Be Described to a Good Approximation Using Atomic Orbitals The Xa Exchange Approximation The Z 1 approximation The Zero-Field Approximation The approximate integration of differential equations The approximation of a -pdf The approximation of a lognormal-pdf The boundary-layer approximation for laminar flows with chemical reactions The centroid molecular dynamics approximation The cluster expansion and super-position approximation The diagonalized quasi-analytical (DQA) approximation The dipole approximation The extended steady-state approximation The flame sheet approximation The high temperature approximation The incoherent approximation The linear approximation The molecular field approximation The nearest-available-neighbour approximation The nearly free electron approximation The orbital approximation The parabolic approximation The parton model as an impulse approximation The perturbation is always large in polarization approximation The pre-equilibrium approximation The pseudo-binary approximation The q-Centroid Approximation The quasi-static approximation The quasi-steady approximation The quasi-steady-state approximation (QSSA) The rate-determining step approximation The rotating wave approximation The shortened superposition approximation The simple current approximation The simple-tree approximation The single-particle approximation The spectator electrons approximation The steady-state and partial-equilibrium approximations The steady-state approximation (SSA) The summarized approximation method The superposition approximation The tight binding approximation The weak acid where both approximations are valid The weak acid where both approximations can be made The weak base where both approximations can be made Tin Orbitals and the Atomic Sphere Approximation Total Energies in the Local Density Approximation Tunneling Corrections Based on the Adiabatic Approximation Two-Electron Terms and the Douglas-Kroll-Hess Approximation Use of the RLS Approximation Use of the Steady-State Approximation Validity of the Approximations Validity of the BO approximation Vibrational Properties Beyond the Harmonic Approximation Within the ZDO approximation