The Cambridge Handbook of Physics Formulas

Index from 'abberration' to 'coexistence curve' 

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aberration (relativistic) [3.24], 65

absolute magnitude [9.29], 179

absorption (Einstein coefficient) [8.118], 173

absorption coefficient (linear) [5.175], 120

accelerated point charge

     bremsstrahlung, 160

     Liénard-Wiechert potentials, 139

     oscillating [7.132], 146

     synchrotron, 159

acceleration

     constant, 68

     dimensions, 16

     due to gravity (value on Earth), 176

     in a rotating frame [3.32], 66

acceptance angle (optical fibre) [8.77], 169

acoustic branch (phonon) [6.37], 129

acoustic impedance [3.276], 83

action (definition) [3.213], 79

action (dimensions), 16

addition of velocities

     Galilean [3.3], 64

     relativistic [3.15], 64

adiabatic

     bulk modulus [5.23], 107

     compressibility [5.21], 107

     expansion (ideal gas) [5.58], 110

     lapse rate [3.294], 84

adjoint matrix

     definition 1 [2.71], 24

     definition 2 [2.80], 25

adjugate matrix [2.80], 25

admittance (definition), 148

advective operator [3.289], 84

Airy

     disk [8.40], 165

     function [8.17], 163

     resolution criterion [8.41], 165

Airy's differential equation [2.353], 43

albedo [5.193], 121

Alfvén speed [7.277], 158

Alfvén waves [7.284], 158

alt-azimuth coordinates, 177

alternating tensor (e_ijk) [2.444], 50

altitude coordinate [9.9], 177

Ampère's law [7.10], 136

ampere (unit), 4

analogue formula [2.259], 36

angle

     aberration [3.24], 65

     acceptance [8.77], 169

     beam solid [7.210], 153

     Brewster's [7.218], 154

     Compton scattering [7.240], 155

     contact (surface tension) [3.340], 88

     Euler [2.101], 26

     Faraday rotation [7.273], 157

     hour (coordinate) [9.8], 177

     Kelvin wedge [3.330], 87

     Mach wedge [3.328], 87

     of deviation [8.73], 169

     of polarisation [8.81], 170

     of separation [3.133], 73

     principal range (inverse trig.), 34

     refraction, 154

     rotation, 26

     Rutherford scattering [3.116], 72

     spherical excess [2.261], 36

     units, 4, 5

å ngström (unit), 5

angular diameter-redshift relation [9.92], 184

Angular momentum, 98

angular momentum

     conservation [4.113], 98

     definition [3.66], 68

     dimensions, 16

     eigenvalues [4.109] [4.109], 98

     ladder operators [4.108], 98

     of rigid body [3.141], 74

     operators

         and other operators [4.23], 91

         definitions [4.105], 98

ANGULAR MOMENTUM ADDITION, 100

ANGULAR MOMENTUM COMMUTATION RELATIONS, 98

angular speed (dimensions), 16

antenna

     beam efficiency [7.214], 153

     effective area [7.212], 153

     power gain [7.211], 153

     temperature [7.215], 153

ANTENNAS, 153

anticommutation [2.95], 26

antihermitian symmetry, 53

antisymmetric matrix [2.87], 25

APERTURE DIFFRACTION, 165

aperture function [8.34], 165

apocentre (of an orbit) [3.111], 71

apparent magnitude [9.27], 179

Appleton-Hartree formula [7.271], 157

arc length [2.280], 39

arccosx

     from arctan [2.234], 34

     series expansion [2.142], 29

 arcoshx (definition) [2.240], 35

 arccotx (from arctan) [2.237], 34

 arcothx (definition) [2.242], 35

arccscx (from arctan) [2.235], 34

arcschx (definition) [2.244], 35

arcsecx (from arctan) [2.236], 34

arsechx (definition) [2.243], 35

arcsinx

     from arctan [2.233], 34

     series expansion [2.142], 29

arsinhx (definition) [2.239], 35

arctanx (series expansion) [2.143], 29

artanhx (definition) [2.241], 35

area

     of circle [2.263], 37

     of cone [2.272], 37

     of cylinder [2.270], 37

     of ellipse [2.268], 37

     of plane triangle [2.255], 36

     of sphere [2.264], 37

     of spherical cap [2.276], 37

     of torus [2.274], 37

area (dimensions), 16

argument (of a complex number) [2.158], 30

arithmetic mean [2.109], 27

arithmetic progression [2.105], 27

associated Laguerre equation [2.349], 43

associated Laguerre polynomials, 96

associated Legendre equation

     and polynomial solutions [2.429], 48

     differential equation [2.345], 43

ASSOCIATED LEGENDRE FUNCTIONS, 48

astronomical constants, 176

ASTRONOMICAL MAGNITUDES, 179

Astrophysics, 175-185

asymmetric top [3.189], 77

atomic

     form factor [6.30], 128

     mass unit, 6, 9

     numbers of elements, 124

     polarisability [7.91], 142

     weights of elements, 124

ATOMIC CONSTANTS, 7

atto, 5

autocorrelation (Fourier) [2.492], 53

autocorrelation function [8.104], 172

availability

     and fluctuation probability [5.131], 116

     definition [5.40], 108

Avogadro constant, 6, 9

Avogadro constant (dimensions), 16

azimuth coordinate [9.10], 177

BALLISTICS, 69

band index [6.85], 134

BAND THEORY AND SEMICONDUCTORS, 134

bandwidth

     and coherence time [8.106], 172

     and Johnson noise [5.141], 117

     Doppler [8.117], 173

     natural [8.113], 173

     of a diffraction grating [8.30], 164

     of an LCR circuit [7.151], 148

     of laser cavity [8.127], 174

     Schawlow-Townes [8.128], 174

bar (unit), 5

barn (unit), 5

BARRIER TUNNELLING, 94

Bartlett window [2.582], 60

base vectors (crystallographic), 126

basis vectors [2.17], 20

Bayes' theorem [2.570], 59

BAYESIAN INFERENCE, 59

bcc structure, 127

beam bowing under its own weight [3.260], 82

beam efficiency [7.214], 153

beam solid angle [7.210], 153

beam with end-weight [3.259], 82

beaming (relativistic) [3.25], 65

becquerel (unit), 4

BENDING BEAMS, 82

bending moment (dimensions), 16

bending moment [3.258], 82

bending waves [3.268], 82

Bernoulli's differential equation [2.352], 43

Bernoulli's equation

     compressible flow [3.292], 84

     incompressible flow [3.290], 84

Bessel equation [2.346], 43

BESSEL FUNCTIONS, 47

beta (in plasmas) [7.278], 158

binomial

     coefficient [2.122], 28

     distribution [2.548], 57

     series [2.121], 28

     theorem [2.123], 28

binormal [2.286], 39

Biot-Savart law [7.9], 136

Biot-Fourier equation [5.95], 113

black hole

     evaporation time [9.81], 183

     Kerr solution [3.62], 67

     maximum angular momentum [9.80], 183

     Schwarzschild radius [9.73], 183

     Schwarzschild solution [3.61], 67

     temperature [9.82], 183

blackbody

     energy density [5.192], 121

     spectral energy density [5.186], 121

     spectrum [5.184], 121

BLACKBODY RADIATION, 121

Bloch's theorem [6.84], 134

Bode's law [9.41], 180

body cone, 77

body frequency [3.187], 77

body-centred cubic structure, 127

Bohr

     energy [4.74], 95

     magneton (equation) [4.137], 100

     magneton (value), 6, 7

     quantisation [4.71], 95

     radius (equation) [4.72], 95

     radius (value), 7

Bohr magneton (dimensions), 16

BOHR MODEL, 95

boiling points of elements, 124

bolometric correction [9.34], 179

Boltzmann

     constant, 6, 9

     constant (dimensions), 16

     distribution [5.111], 114

     entropy [5.105], 114

     excitation equation [5.125], 116

Born collision formula [4.178], 104

Bose condensation [5.123], 115

Bose-Einstein distribution [5.120], 115

boson statistics [5.120], 115

BOUNDARY CONDITIONS FOR E, D, B AND H, 144

box (particle in a) [4.64], 94

Box Muller transformation [2.562], 58

Boyle temperature [5.66], 110

Boyle's law [5.56], 110

bra vector [4.33], 92

bra-ket notation, 91, 92

Bragg's reflection law (in crystals) [6.29], 128

Bragg's reflection law (in optics) [8.32], 164

braking index (pulsar) [9.66], 182

BRAVAIS LATTICES, 126

Breit-Wigner formula [4.174], 104

BREMSSTRAHLUNG, 160

bremsstrahlung

     single electron and ion [7.297], 160

     thermal [7.300], 160

Brewster's law [7.218], 154

brightness (blackbody) [5.184], 121

Brillouin function [4.147], 101

Bromwich integral [2.519], 55

Brownian motion [5.98], 113

bubbles [3.337], 88

bulk modulus

     adiabatic [5.23], 107

     general [3.245], 81

     isothermal [5.22], 107

bulk modulus (dimensions), 16

BULK PHYSICAL CONSTANTS, 9

Burgers vector [6.21], 128

calculus of variations [2.335], 42

candela, 119

candela (unit), 4

canonical

     ensemble [5.111], 114

     entropy [5.106], 114

     equations [3.220], 79

     momenta [3.218], 79

cap, see spherical cap

CAPACITANCE, 137

capacitance

     current through [7.144], 147

     definition [7.143], 147

     dimensions, 16

     energy [7.153], 148

     energy of an assembly [7.134], 146

     impedance [7.159], 148

     mutual [7.134], 146

capacitance of

     cube [7.17], 137

     cylinder [7.15], 137

     cylinders (adjacent) [7.21], 137

     cylinders (coaxial) [7.19], 137

     disk [7.13], 137

     disks (coaxial) [7.22], 137

     nearly spherical surface [7.16], 137

     sphere [7.12], 137

     spheres (adjacent) [7.14], 137

     spheres (concentric) [7.18], 137

capacitor, see capacitance

capillary

     constant [3.338], 88

     contact angle [3.340], 88

     rise [3.339], 88

     waves [3.321], 86

capillary-gravity waves [3.322], 86

cardioid [8.46], 166

Carnot cycles, 107

Cartesian coordinates, 21

Catalan's constant (value), 9

Cauchy

     differential equation [2.351], 43

     distribution [2.556], 58

     inequality [2.152], 30

     integral formula [2.168], 31

Cauchy-Goursat theorem [2.166], 31

Cauchy-Riemann conditions [2.165], 31

cavity modes (laser) [8.124], 174

Celsius (unit), 4

Celsius conversion [1.1], 15

centi, 5

centre of mass

     circular arc [3.173], 76

     cone [3.175], 76

     definition [3.68], 68

     disk sector [3.172], 76

     hemisphere [3.170], 76

     hemispherical shell [3.171], 76

     pyramid [3.175], 76

     semi-ellipse [3.178], 76

     spherical cap [3.177], 76

     triangular lamina [3.174], 76

CENTRES OF MASS, 76

centrifugal force [3.35], 66

centripetal acceleration [3.32], 66

cepheid variables [9.48], 180

Cerenkov, see Cherenkov

chain rule

     function of a function [2.296], 40

     partial derivatives [2.332], 42

Chandrasekhar mass [9.79], 183

change of variable [2.334], 42

CHARACTERISTIC NUMBERS, 86

charge

     conservation [7.39], 139

     dimensions, 16

     elementary, 6, 7

     force between two [7.119], 145

     Hamiltonian [7.138], 146

     to mass ratio of electron, 8

charge density

     dimensions, 16

     free [7.57], 140

     induced [7.84], 142

     Lorentz transformation, 141

charge distribution

     electric field from [7.6], 136

     energy of [7.133], 146

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

Chebyshev equation [2.350], 43

Chebyshev inequality [2.151], 30

chemical potential

     definition [5.28], 108

     from partition function [5.119], 115

Cherenkov cone angle [7.246], 156

CHERENKOV RADIATION, 156

c_E (electric susceptibility) [7.87], 142

c_H, c_B (magnetic susceptibility) [7.103], 143

chi-squared (c²) distribution [2.554], 58

Christoffel symbols [3.49], 67

circle

     (arc of) centre of mass [3.173], 76

     area [2.263], 37

     perimeter [2.262], 37

circular aperture

     Fraunhofer diffraction [8.40], 165

     Fresnel diffraction [8.50], 166

circular polarisation, 170

circulation [3.287], 84

civil time [9.4], 177

Clapeyron equation [5.50], 109

classical electron radius, 8

Classical thermodynamics, 106

Clausius-Mossotti equation [7.93], 142

Clausius-Clapeyron equation [5.49], 109

CLEBSCH-GORDAN COEFFICIENTS, 99

Clebsch-Gordan coefficients (spin-orbit) [4.136], 100

close-packed spheres, 127

closure density (of the universe) [9.98], 185

CNO cycle, 182

coaxial cable

     capacitance [7.19], 137

     inductance [7.24], 137

coaxial transmission line [7.181], 150

coefficient of

     coupling [7.148], 147

     finesse [8.12], 163

     reflectance [7.227], 154

     reflection [7.230], 154

     restitution [3.127], 73

     transmission [7.232], 154

     transmittance [7.229], 154

coexistence curve [5.51], 109