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morse p methods theoretical physics part ii 1953

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Textbook in PDF format Approximate Methods The Usual Perturbation Formula Convergence Of Series Multidimensional Problems An Example Feenberg Perturbation Formula; Secular Determinant An Example Fredholm Perturbation Formula An Example Variation-Iteration Method Convergence Of The Method An Example Improved Perturbation Formulas Nonorthogonal Functions Boundary Perturbations Perturbation Of Boundary Conditions, f Small Perturbation Of Boundary Conditions, f Large An Example Formulas For Small w Long, Narrow Rectangle Perturbation Of Boundary Shape Evaluation Of Integrals Convergence Improving The Convergence Perturbation Of Boundaries For Dirichlet Conditions A Special Class Of Boundary Perturbation Perturbation Methods For Scattering And Diffraction Boundary Conditions For Scattering Scattering From A Spherically Symmetric Region-Phase Shifts Integral Equation For Scattering Integral Equation For One-Dimensional Problems Integral Equation For Three Dimensions Born Approximation Higher Born Approximations Fredholm Series An Example A Three-Dimensional Example Long-Wavelength Approximation Long-Wavelength Approximation For The Schroedinger Equation Convergence Short-Wavelength-Approximation;WKBJ Method Relation To Integral Equation Case Of Well-Separated Classical Turning Points WKBJ Method For Bound Systems Penetration Through A Barrier WKBJ Phase Shifts Case Of Closely Spaced Classical Turning-Points Short-Wavelength Approximation In Three Dimensions Variational Methods Variational Principle For Eigenvalue Problems Variational Principles For Resonant Frequencies And Energy Levels Vibration Of A Circular Membrane Rayleigh-Ritz Method Application To Perturbation Theory Integral Equation And Corresponding Variational Principle An Example Variational Principle For Phase Shifts Variational Principle For The Phase Shift, Based On An Integral Equation Variational Principle For The Transmission Amplitude Variational Principle For Three-Dimensional Scattering Problems Variational Principles For Surface Perturbations Variational Principle Based On The Integral Equation For Boundary Perturbations Scattering From Surfaces A Variational Principle For Radiation Problems Variation-Iteration Method An Extrapolation Method Lower Bounds For lambda-naught Comparison Method for Lower Bounds L Not Positive-Definite Variational Methods For The Higher Eigenvalues Method Of Minimized Iterations Problems For Tabulation Of Approximation Methods Bibliography Solutions Of Laplace's And Poisson's Equations Cartesian Coordinates Rectangular Prism Heated On One Side Green's Function Polar Coordinates Cylinders Placed In Fields Flow Of Viscous Liquids Green's Function In Polar Coordinates Internal Heating Of Cylinders Potential Near A Slotted Cylinder Elliptic Coordinates Viscous Flow Through A Slit Elliptic Cylinders In Uniform Fields Green's Function For Elliptic Coordinates Potential Inside A Cylinder With Narrow Slot Parabolic Coordinates Bipolar Coordinates Two Cylinders In A Uniform Field Green's Function In Bipolar Coordinates Complex Variables And The Two-Dimensional Laplace Equation Fields, Boundary Conditions, And Analytic Functions Some Elementary Solutions Transformation Of Solutions Circulation And Lift Fields Due To Distributions Of Line Sources Grid Potentials And Amplification Factors Linear Arrays Of Source Lines Two-dimensional Array Of Line Sources Periodic Distributions Of Images Potentials About Prisms Parallel-Plate Condenser Variable Condenser Other Rectangular Shapes Solutions For Three Dimensions Integral Form For The Green's Function Solutions In Rectangular Coordinates Solutions In Circular Cylindrical Coordinates Integral Representation For The Eigenfunction Green's Function For Interior Field Solutions In Spherical Coordinates Fields Of Charged Disks And From Currents In Wire Loops Fields Of Charged Spherical Caps Integral Representation Of Solutions The Green's Function Expansion Dipoles, Quadrupoles,And Multipoles Spherical Shell With Hole Prolate Spheroidal Coordinates Integral Representations For Spheroidal Solutions Green's Function For Prolate Spheroids Oblate Spheroids Flow through An Orifice Integral Representations And Green's Functions Parabolic Coordinates Bispherical Coordinates Toroidal Coordinates Ellipsoidal Coordinates Problems For Trigonometric And Hyperbolic Functions Bessel Functions Legendre Functions Bibliography The Wave Equation Wave Motion In One Space Dimension Fourier Transforms String With Friction Laplace Transform String With Friction String With Elastic Support String With Nonrigid Supports Reflection From A Frictional Support Sound Waves In A Tube Tube With A Varying Cross Section Acoustic Circuit Elements Free-Wave Representations Movable Supports Waves In Two Space Dimensions Fourier Transforms And Green's Functions Rectangular Coordinates Other Boundary Conditions Variable Boundary Admittance Polar Coordinates Waves Inside A Circular Boundary Radiation From A Circular Boundary Scattering Of Plane Wave From Cylinder Scattered And Reflected Wave Short And Long- Wavelength Limits Scattering Of Plane Waves From A Knife Edge Fresnel Diffraction From Knife Edge Scattering From A Cylinder With Slit Slotted Cylinder, Neumann Conditions Waves In Parabolic Coordinates Eigenfunctions For Interior Problems Waves Outside Parabolic Boundaries Green's Function And Plane Wave Expansions Elliptic Coordinates The Radial Solutions Approximations For Small Values Of h And m Approximations For h Small And m Large Expressions For h Large Waves Inside An Elliptic Boundary Green's Function And Plane Wave Expansions Radiation From A Vibrating Strip Radiation From A Strip Carrying Current Scattering Of Waves From Strips Diffraction Through A Slit, Babinet's Principle Waves In Three Space Dimensions Green's Function For Free Space Rectangular Enclosure Distortion Of Standing Wave By Strip Computing The Eigenvalue Transmission Through Ducts Acoustic Transients In A Rectangular Duct Constriction In Rectangular Duct Wave Transmission Around Comer Membrane In Circular Radiation From Tube Termination Transmission In Elastic Tubes Spherical Coordinates Spherical Bessel Functions Green's Function And Plane Wave Expansion Waves Inside A Sphere Vibrations Of A Hollow, Flexible Sphere Vibrating String In Sphere Resonance Frequencies Of The System Radiation From Sphere Dipole Source Radiation From A Collection Of Sources Radiation From Piston In Sphere Scattering Of Plane Waves From Sphere Scattering From A Sphere With Complex Index Of Refraction Scattering From A Helmholtz Resonator Scattering From An Ensemble Of Scatterers Scattering Of Sound From Air Bubbles In Water Spheroidal Coordinates The Radial Functions Green's Function And Other Expansions Oblate Spheroidal Coordinates Integral And Variational Techniques Iris Diaphragm In Pipe A Variational Principle Calculating The Transmission Factor Hole In Infinite Plane Reflection In Lined Duct Fourier Transform Of The Integral Equation Factoring The Transformed Equation Radiation From End Of Circular Pipe Formulas For Power Radiated And Reflected The Fourier Transform Of The Integral Equation Factoring The Transformed Equation Radiation From Vibrating Source Angle Distribution Of Radiated Wave Applying The Boundary Conditions Scattering Of Waves, Variational Principle Angle -Distribution Function And Total Cross Section Scattering From Spheres Scattering From A Strip Scattering Of Short Waves Problems For Cylindrical Bessel Functions Weber Functions Mathieu Functions Spherical Bessel Functions Spheroidal Functions Short Table Of Laplace Transforms Bibliography Solutions Of The Diffusion Equation Transient Surface Heating Of A Slab Green's Functions And Image Sources Radiative Heating Transient Internal Heating Of A Slab Diffusion And Absorption Of Particles Fission And Diffusion Laplace Transform Solution The Slowing-Down Of Particles Fission, Diffusion, And Slowing-Down General Case, Diffusion Approximation Heating Of A Sphere Distribution Functions For Diffusion Problems Uniform Space Distribution Approximations For Forward Scattering General Considerations, Steady-State Case Integral Relations Between Tthe Variables Calculating The Diffuse Scattering Calculating The Diffuse Emission Solution By Laplace Transforms The Variational Calculation Of Density Loss Of Energy On Collision Uniform Space Distribution Age Theory Definitions The Harmonic Oscillator Short-Range Forces The Effect Of A Perturbation Approximate Formulas For General Perturbation Momentum Wave Functions Bound And Free States Existence Of Bound States Reflection And Transmission Penetration Through A Potential Barrier Central Force Fields, Angular Momentum Central Force Fields, The Radial Equation Coulomb Potential Inverse Cube Force Coulomb Field In Parabolic Coordinates Rutherford Scattering Other Soluble Central Force Systems Perturbations Of Degenerate Systems The Stark Effect Momentum Eigenfunctions Scattering From Central Fields Ramsauer And Other Resonance Effects Approximate Calculations For Slow Incident Particles The Born Approximation Phase Angles By Born Approximation The Variation Method Variation-Iteration Method Variational Principles For Scattering Variation-Iteration Method For Scattering Variational Principle For The Angle Distribution Two Particles, One-Dimensional Case The Green's Function Surface Waves The Effects Of Interaction Between The Particles Meaning Of The Results Coupled Harmonic Oscillators Central Force Fields, Several Particles, Angular Momentum Inversion And Parity Symmetrizing For Two-Particle Systems Bound, Free, And "Surface" States Green's Function For The Two-Particle System Bound States Variational Calculation Scattering Of Electron From Hydrogen Atom Elastic And Inelastic Scattering Exchange Of Particles Problems For Jacobi Polynomials Semicylindrical Functions Bibliography Vector Fields Vector Boundary Conditions, Eigenfunctions, And Green'sFunctions The Transverse Field In Curvilinear Coordinates Vector Green's Theorems The Green's Function A Dyadic Vector Eigenfunctions Green's Function For The Vector Helmholtz Equation Longitudinal And Transverse Green's Dyadics Green's Dyadic For Elastic Waves Solutions Of The Vector Laplace Equation Green's Functions For The Wave Equation Static And Steady-State Solutions Two-Dimensional Solutions Polar Coordinates Circular Cylinder Coordinates Spherical Coordinates Green's Dyadic For Vector Laplace Equation Magnetic Field Solutions Viscous Flow about a Sphere Elastic Distortion Of A Sphere Tractions Specified On Surface Reflection Of Plane Waves From A Plane Boundary Impedance Elastic Wave Reflection Waves In A Duct The Green's Function Generation Of Waves by Wire Losses Along The Duct Walls Reflection Of Waves From End Of Tube Effect Of Change Of Duct Size Elastic Waves Along A Bar Torsional Forced Motions Of A Rod Nonstationary Viscous Flow In Tube Electromagnetic Resonators Energy Loss At The Walls, The Q Of The Cavity Excitation Of Resonator By Driving Current Excitation By Wave Guide Resonance Frequencies Of A Klystron Cavity Scattering From Cylinders Spherical Waves Radiation From Dipoles And Multipoles Standing Waves In A Spherical Enclosure Vibrations Of An Elastic Sphere The Green's Function For Free Space Radiation From A Vibrating Current Distribution Radiation From A Half-wave Antenna Radiation From A Current Loop Scattering From A Sphere Energy Absorption By The Sphere Distortion Of Field By Small Object Problems For Table Of Spherical Vector Harmonics Bibliography Appendix Glossary Of Symbols Used Glossary Table I Trigonometric And Hyperbolic Functions Table II Trigonometric And Hyperbolic Functions Table III Hyperbolic Tangent Of Complex Quantity Table IV Inverse Hyperbolic Tangent Of Complex Quantity Table V Logarithmic And Inverse Hyperbolic Functions Table VI Spherical Harmonic Functions Table VII Legendre Functions For Large Arguments Table VIII Legendre Functions For Imaginary Arguments Table IX Legendre Functions Of Half-Integral Degree Table X Bessel Functions For Cylindrical Coordinates Table XI Hyperbolic Bessel Functions Table XII Bessel Functions For Spherical Coordinates Table XIII Legendre Functions For Spherical Coordinates Table XIV Amplitudes And Phases For Cylindrical Bessel Functions Table XIV Amplitudes And Phases For Cylindrical Bessel Functions Table XIV Amplitudes And Phases For Cylindrical Bessel Functions (continued) Table XV Amplitudes And Phases For Spherical Bessel Functions Table XV Amplitudes And Phases For Spherical Bessel Functions (continued) Table XV Amplitudes And Phases For Spherical Bessel Functions (continued) Table XVI Periodic Mathieu Functions Table XVI Periodic Mathieu Functions-(continued) Table XVII Normalizing Constants For Periodic Mathieu Functions And Limiting Values Of Radial Mathieu Functions Table XVII Normalizing Constants For Periodic Mathieu Functions And Limiting Values Of Radial Mathieu Functions (continued) Bibliography Index Back Cover

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Morse P. Methods Of Theoretical Physics Part II 1953.pdf 19.6 MB

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morse p methods theoretical physics part ii 1953

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