The Cambridge Handbook of Physics Formulas

Index from 'saddle point' to 'zone law' 

---

saddle point, 42

Saha equation (general) [5.128], 116

Saha equation (ionisation) [5.129], 116

Saturn data, 176

scalar effective mass [6.87], 134

scalar product [2.1], 20

scalar triple product [2.10], 20

scattering

     angle (Rutherford) [3.116], 72

     Born approximation [4.178], 104

     Compton [7.240], 155

     crystal [6.32], 128

     inverse Compton [7.239], 155

     Klein-Nishina [7.243], 155

     Mott (identical particles) [4.180], 104

     potential (Rutherford) [3.114], 72

     processes (electron), 155

     Rayleigh [7.236], 155

     Rutherford [3.124], 72

     Thomson [7.238], 155

scattering cross-section, see cross-section

Schawlow-Townes line width [8.128], 174

Schrödinger equation [4.15], 90

Schwarz inequality [2.153], 30

Schwarzschild geometry (in GR) [3.61], 67

Schwarzschild radius [9.73], 183

Schwarzschild's equation [5.179], 120

screw dislocation [6.22], 128

secx

     definition [2.229], 34

     series expansion [2.139], 29

secant method (of root-finding) [2.593], 61

sechx [2.230], 34

second (of time), 4

second (unit), 5

second moment of area [3.258], 82

Sedov-Taylor shock relation [3.331], 87

selection rules (dipole transition) [4.91], 96

self-diffusion [5.93], 113

self-inductance [7.145], 147

semi-ellipse (centre of mass) [3.178], 76

semi-empirical mass formula [4.173], 103

semi-latus-rectum [3.109], 71

semi-major axis [3.106], 71

semi-minor axis [3.107], 71

semiconductor diode [6.92], 134

semiconductor equation [6.90], 134

SERIES EXPANSIONS, 29

series impedances [7.157], 148

Series, summations and progressions, 27

shah function (Fourier transform of) [2.511], 54

shear

     modulus [3.249], 81

     strain [3.237], 80

     viscosity [3.299], 85

     waves [3.262], 82

shear modulus (dimensions), 17

sheet of charge (electric field) [7.32], 138

shift theorem (Fourier transform) [2.502], 54

shock

     Rankine-Hugoniot conditions [3.334], 87

     spherical [3.331], 87

SHOCKS, 87

shot noise [5.142], 117

SI BASE UNITS, 4

SI DERIVED UNITS, 4

SI PREFIXES, 5

SI units, 4

sidelobes (diffraction by 1-D slit) [8.38], 165

sidereal time [9.7], 177

siemens (unit), 4

sievert (unit), 4

similarity theorem (Fourier transform) [2.501], 54

simple cubic structure, 127

simple harmonic oscillator, see harmonic oscillator

simple pendulum [3.179], 76

Simpson's rule [2.587], 61

sinx

     and Euler's formula [2.219], 34

     series expansion [2.137], 29

sinc function [2.512], 54

sine formula

     planar triangles [2.247], 36

     spherical triangles [2.256], 36

sinhx

     definition [2.220], 34

     series expansion [2.145], 29

sin^-1 x, see arccosx

skew-symmetric matrix [2.87], 25

skewness estimator [2.545], 57

skin depth [7.235], 155

slit diffraction (broad slit) [8.37], 165

slit diffraction (Young's) [8.24], 164

Snell's law (acoustics) [3.284], 83

Snell's law (electromagnetism) [7.217], 154

soap bubbles [3.337], 88

solar constant, 176

SOLAR DATA, 176

Solar system data, 176

solenoid

     finite [7.38], 138

     infinite [7.33], 138

     self inductance [7.23], 137

solid angle (subtended by a circle) [2.279], 37

Solid state physics, 123-134

sound speed (in a plasma) [7.275], 158

sound, speed of [3.317], 86

space cone, 77

space frequency [3.188], 77

space impedance [7.197], 152

spatial coherence [8.108], 172

Special functions and polynomials, 46

special relativity, 64

specific

     charge on electron, 8

     emission coefficient [5.174], 120

     heat capacities, see heat capacity

     intensity (blackbody) [5.184], 121

     intensity [5.171], 120

specific heat capacity, see heat capacity

     definition, 105

     dimensions, 17

specific impulse [3.92], 70

speckle intensity distribution [8.110], 172

speckle size [8.111], 172

spectral energy density

     blackbody [5.186], 121

     definition [5.173], 120

spectral function (synchrotron) [7.295], 159

SPECTRAL LINE BROADENING, 173

speed (dimensions), 17

speed distribution (Maxwell-Boltzmann) [5.84], 112

speed of light (equation) [7.196], 152

speed of light (value), 6

speed of sound [3.317], 86

sphere

     area [2.264], 37

     Brownian motion [5.98], 113

     capacitance [7.12], 137

     capacitance of adjacent [7.14], 137

     capacitance of concentric [7.18], 137

     close-packed, 127

     collisions of, 73

     electric field [7.27], 138

     geometry on a, 36

     gravitation field from a [3.44], 66

     in a viscous fluid [3.308], 85

     in potential flow [3.298], 84

     moment of inertia [3.152], 75

     Poincaré, 171

     polarisability, 142

     volume [2.265], 37

spherical Bessel function [2.421], 47

spherical cap

     area [2.276], 37

     centre of mass [3.177], 76

     volume [2.277], 37

spherical excess [2.261], 36

SPHERICAL HARMONICS, 49

spherical harmonics

     definition [2.437], 49

     Laplace equation [2.441], 49

     orthogonality [2.438], 49

spherical polar coordinates, 21

spherical shell (moment of inertia) [3.153], 75

spherical surface (capacitance of near) [7.16], 137

SPHERICAL TRIANGLES, 36

spin

     and total angular momentum [4.128], 100

     degeneracy, 115

     electron magnetic moment [4.141], 100

     Pauli matrices, 26

spinning bodies, 77

spinors [4.182], 104

Spitzer conductivity [7.254], 156

spontaneous emission [8.119], 173

spring constant and wave velocity [3.272], 83

SQUARE MATRICES, 25

STANDARD COSMOLOGICAL MODELS, 185

standard deviation estimator [2.544], 57

STANDARD FORMS, 44

STAR FORMATION, 181

STAR-DELTA TRANSFORMATION, 149

Static fields, 136

statics, 63

STATIONARY POINTS, 42

STATISTICAL ENTROPY, 114

Statistical thermodynamics, 114

Stefan-Boltzmann constant, 9, 121

Stefan-Boltzmann constant (dimensions), 17

Stefan-Boltzmann law [5.191], 121

stellar aberration [3.24], 65

Stellar evolution, 181

STELLAR FUSION PROCESSES, 182

STELLAR THEORY, 181

step function (Fourier transform of) [2.511], 54

steradian (unit), 4

stimulated emission [8.120], 173

Stirling's formula [2.412], 46

STOKES PARAMETERS, 171

Stokes parameters [8.95], 171

Stokes's law [3.308], 85

Stokes's theorem [2.60], 23

STRAIGHT-LINE FITTING, 60

strain

     simple [3.229], 80

     tensor [3.233], 80

     volume [3.236], 80

stress

     dimensions, 17

     in fluids [3.299], 85

     simple [3.228], 80

     tensor [3.232], 80

stress-energy tensor

     and field equations [3.59], 67

     perfect fluid [3.60], 67

string (waves along a stretched) [3.273], 83

Strouhal number [3.313], 86

structure factor [6.31], 128

sum over states [5.110], 114

SUMMARY OF PHYSICAL CONSTANTS, 6

summation formulae [2.119], 27

Sun data, 176

Sunyaev-Zel'dovich effect [9.51], 180

surface brightness (blackbody) [5.184], 121

surface of revolution [2.281], 39

SURFACE TENSION, 88

surface tension

     Laplace's formula [3.337], 88

     work done [5.6], 106

surface tension (dimensions), 17

surface waves [3.320], 86

survival equation (for mean free path) [5.90], 113

susceptance (definition), 148

susceptibility

     electric [7.87], 142

     Landau diamagnetic [6.80], 133

     magnetic [7.103], 143

     Pauli paramagnetic [6.79], 133

symmetric matrix [2.86], 25

symmetric top [3.188], 77

SYNCHROTRON RADIATION, 159

synodic period [9.44], 180

tanx

     definition [2.221], 34

     series expansion [2.138], 29

tangent [2.284], 39

tangent formula [2.251], 36

tanhx

     definition [2.222], 34

     series expansion [2.146], 29

tan^-1 x, see arctanx

Taylor series

     one-dimensional [2.124], 28

     three-dimensional [2.125], 28

telegraphist's equations [7.171], 150

temperature

     antenna [7.215], 153

     Celsius, 4

     dimensions, 17

     Kelvin scale [5.2], 106

     thermodynamic [5.1], 106

TEMPERATURE CONVERSIONS, 15

temporal coherence [8.105], 172

tensor

     Einstein [3.58], 67

     electric susceptibility [7.87], 142

     e_ijk[2.444], 50

     fluid stress [3.299], 85

     magnetic susceptibility [7.103], 143

     moment of inertia [3.136], 74

     Ricci [3.57], 67

     Riemann [3.50], 67

     strain [3.233], 80

     stress [3.232], 80

tera, 5

tesla (unit), 4

tetragonal system (crystallographic), 127

tetrahedron, 38

thermal conductivity

     diffusion equation [2.341], 43

     dimensions, 17

     free electron [6.65], 132

     phonon gas [6.58], 131

     transport property [5.96], 113

thermal de Broglie wavelength [5.83], 112

thermal diffusion [5.93], 113

thermal diffusivity [2.341], 43

thermal noise [5.141], 117

thermal velocity (electron) [7.257], 156

THERMODYNAMIC COEFFICIENTS, 107

THERMODYNAMIC FLUCTUATIONS, 116

THERMODYNAMIC LAWS, 106

THERMODYNAMIC POTENTIALS, 108

thermodynamic temperature [5.1], 106

THERMODYNAMIC WORK, 106

Thermodynamics, 105-121

THERMOELECTRICITY, 133

thermopower [6.81], 133

Thomson cross-section, 8

Thomson scattering [7.238], 155

throttling process [5.27], 108

time (dimensions), 17

time dilation [3.11], 64

TIME IN ASTRONOMY, 177

TIME SERIES ANALYSIS, 60

TIME-DEPENDENT PERTURBATION THEORY, 102

TIME-INDEPENDENT PERTURBATION THEORY, 102

timescale

     free-fall [9.53], 181

     Kelvin-Helmholtz [9.55], 181

Titius-Bode rule [9.41], 180

tonne (unit), 5

top

     asymmetric [3.189], 77

     symmetric [3.188], 77

     symmetries [3.149], 74

top hat function (Fourier transform of) [2.512], 54

TOPS AND GYROSCOPES, 77

torque, see couple

TORSION, 81

torsion

     in a thick cylinder [3.254], 81

     in a thin cylinder [3.253], 81

     in an arbitrary ribbon [3.256], 81

     in an arbitrary tube [3.255], 81

     in differential geometry [2.289], 39

torsional pendulum [3.181], 76

torsional rigidity [3.252], 81

torus (surface area) [2.274], 37

torus (volume) [2.275], 37

total differential [2.330], 42

total internal reflection [7.217], 154

total width (and partial widths) [4.176], 104

trace [2.75], 25

trajectory (of projectile) [3.88], 69

transfer equation [5.179], 120

TRANSFORMERS, 149

transmission coefficient

     Fresnel [7.232], 154

     potential barrier [4.59], 94

     potential step [4.42], 92

     potential well [4.49], 93

transmission grating [8.27], 164

transmission line, 150

     coaxial [7.181], 150

     equations [7.171], 150

     impedance

         lossless [7.174], 150

         lossy [7.175], 150

     input impedance [7.178], 150

     open-wire [7.182], 150

     paired strip [7.183], 150

     reflection coefficient [7.179], 150

     vswr [7.180], 150

     wave speed [7.176], 150

     waves [7.173], 150

TRANSMISSION LINE IMPEDANCES, 150

TRANSMISSION LINE RELATIONS, 150

Transmission lines and waveguides, 150

transmittance coefficient [7.229], 154

TRANSPORT PROPERTIES, 113

transpose matrix [2.70], 24

trapezoidal rule [2.586], 61

triangle

     area [2.255], 36

     centre of mass [3.174], 76

     inequality [2.148], 30

     plane, 36

     spherical, 36

triangle function (Fourier transform of) [2.513], 54

triclinic system (crystallographic), 127

trigonal system (crystallographic), 127

TRIGONOMETRIC AND HYPERBOLIC DEFINITIONS, 34

Trigonometric and hyperbolic formulae, 32

TRIGONOMETRIC AND HYPERBOLIC INTEGRALS, 45

TRIGONOMETRIC DERIVATIVES, 41

TRIGONOMETRIC RELATIONSHIPS, 32

triple-a process, 182

tube, see pipe

Tully-Fisher relation [9.49], 180

tunnelling (quantum mechanical), 94

tunnelling probability [4.61], 94

turns ratio (of transformer) [7.163], 149

two-level system (microstates of) [5.107], 114

U (Stokes parameter) [8.92], 171

U B V magnitude system [9.36], 179

umklapp processes [6.59], 131

uncertainty relation

     energy-time [4.8], 90

     general [4.6], 90

     momentum-position [4.7], 90

     number-phase [4.9], 90

underdamping [3.198], 78

unified atomic mass unit, 5, 6

uniform distribution [2.551], 58

uniform to normal distribution transformation, 58

unitary matrix [2.88], 25

units (conversion of SI to Gaussian), 135

Units, constants and conversions, 3-18

universal time [9.4], 177

Uranus data, 176

UTC [9.4], 177

V (Stokes parameter) [8.94], 171

van der Waals equation [5.67], 111

VAN DER WAALS GAS, 111

van der Waals interaction [6.50], 131

Van-Cittert Zernicke theorem [8.108], 172

variance estimator [2.543], 57

variations, calculus of [2.335], 42

VECTOR ALGEBRA, 20

VECTOR INTEGRAL TRANSFORMATIONS, 23

vector product [2.2], 20

vector triple product [2.12], 20

Vectors and matrices, 20

velocity (dimensions), 17

velocity distribution (Maxwell-Boltzmann) [5.84], 112

velocity potential [3.296], 84

VELOCITY TRANSFORMATIONS, 64

Venus data, 176

virial coefficients [5.65], 110

VIRIAL EXPANSION, 110

virial theorem [3.102], 71

viscosity

     dimensions, 17

     from kinetic theory [5.97], 113

     kinematic [3.302], 85

     shear [3.299], 85

viscous flow

     between cylinders [3.306], 85

     between plates [3.303], 85

     through a circular pipe [3.305], 85

     through an annular pipe [3.307], 85

VISCOUS FLOW (INCOMPRESSIBLE), 85

volt (unit), 4

voltage

     across an inductor [7.146], 147

     bias [6.92], 134

     Hall [6.68], 132

     law (Kirchhoff's) [7.162], 149

     standing wave ratio [7.180], 150

     thermal noise [5.141], 117

     transformation [7.164], 149

volume

     dimensions, 17

     of cone [2.273], 37

     of cube, 38

     of cylinder [2.271], 37

     of dodecahedron, 38

     of ellipsoid [2.269], 37

     of icosahedron, 38

     of octahedron, 38

     of parallelepiped [2.10], 20

     of pyramid [2.273], 37

     of revolution [2.282], 39

     of sphere [2.265], 37

     of spherical cap [2.277], 37

     of tetrahedron, 38

     of torus [2.275], 37

volume expansivity [5.19], 107

volume strain [3.236], 80

vorticity and Kelvin circulation [3.287], 84

vorticity and potential flow [3.297], 84

vswr [7.180], 150

wakes [3.330], 87

WARM PLASMAS, 156

watt (unit), 4

wave equation [2.343], 43

wave impedance

     acoustic [3.276], 83

     electromagnetic [7.198], 152

     in a waveguide [7.189], 151

Wave mechanics, 92

WAVE SPEEDS, 87

wavefunction

     and expectation value [4.25], 91

     and probability density [4.10], 90

     diffracted in 1-D [8.34], 165

     hydrogenic atom [4.91], 96

     perturbed [4.160], 102

WAVEFUNCTIONS, 90

waveguide

     cut-off frequency [7.186], 151

     equation [7.185], 151

     impedance

         TE modes [7.189], 151

         TM modes [7.188], 151

     TE_mn modes [7.190], 151

     TM_mn modes [7.192], 151

     velocity

         group [7.188], 151

         phase [7.187], 151

WAVEGUIDES, 151

wavelength

     Compton [7.240], 155

     de Broglie [4.2], 90

     photometric, 179

     redshift [9.87], 184

     thermal de Broglie [5.83], 112

waves

     capillary [3.321], 86

     electromagnetic, 152

     in a spring [3.272], 83

     in a thin rod [3.271], 82

     in bulk fluids [3.265], 82

     in fluids, 86

     in infinite isotropic solids [3.264], 82

     magnetosonic [7.285], 158

     on a stretched sheet [3.274], 83

     on a stretched string [3.273], 83

     on a thin plate [3.268], 82

     sound [3.317], 86

     surface (gravity) [3.320], 86

     transverse (shear) Alfvén [7.284], 158

Waves in and out of media, 152

WAVES IN LOSSLESS MEDIA, 152

WAVES IN STRINGS AND SPRINGS, 83

wavevector (dimensions), 17

weber (unit), 4

WEBER SYMBOLS, 126

weight (dimensions), 17

Weiss constant [7.114], 144

Weiss zone equation [6.10], 126

Welch window [2.583], 60

Weyl equation [4.182], 104

Wiedemann-Franz law [6.66], 132

Wien's displacement law [5.189], 121

Wien's displacement law constant, 9

Wien's radiation law [5.188], 121

Wiener-Khintchine theorem

     in Fourier transforms [2.493], 53

     in temporal coherence [8.105], 172

Wigner coefficients (spin-orbit) [4.136], 100

Wigner coefficients (table of), 99

windowing

     Bartlett [2.582], 60

     Hamming [2.585], 60

     Hanning [2.584], 60

     Welch [2.583], 60

wire

     electric field [7.29], 138

     magnetic flux density [7.34], 138

wire loop (inductance) [7.26], 137

wire loop (magnetic flux density) [7.37], 138

wires (inductance of parallel) [7.25], 137

work (dimensions), 17

X-ray diffraction, 128

yocto, 5

yotta, 5

Young modulus

     and Lamé coefficients [3.240], 81

     and other elastic constants [3.250], 81

     Hooke's law [3.230], 80

Young modulus (dimensions), 17

Young's slits [8.24], 164

Yukawa potential [7.252], 156

Zeeman splitting constant, 7

zepto, 5

zero-point energy [4.68], 95

zetta, 5

zone law [6.20], 126