The Cambridge Handbook of Physics Formulas

Index from 'Kirchhoff's law' to 'ordinary modes' 

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Kirchhoff's (radiation) law [5.180], 120

KIRCHHOFF'S DIFFRACTION FORMULA, 166

KIRCHHOFF'S LAWS, 149

Klein-Gordon equation [4.181], 104

Klein-Nishina cross-section [7.243], 155

Knudsen flow [5.99], 113

Kronecker delta [2.443], 50

kurtosis estimator [2.546], 57

ladder operators (angular momentum) [4.108], 98

Lagrange's identity [2.7], 20

Lagrangian (dimensions), 17

LAGRANGIAN DYNAMICS, 79

Lagrangian of

     charged particle [3.217], 79

     particle [3.216], 79

     two mutually attracting bodies [3.85], 69

Laguerre equation [2.348], 43

Laguerre polynomials (associated), 96

Lamé coefficients [3.240], 81

LAMINAR VISCOUS FLOW, 85

Landé g-factor [4.146], 100

Landau diamagnetic susceptibility [6.80], 133

Landau length [7.249], 156

Langevin function (from Brillouin fn) [4.147], 101

Langevin function [7.111], 144

Laplace equation

     definition [2.340], 43

     solution in spherical harmonics [2.441], 49

Laplace series [2.440], 49

Laplace transform

     convolution [2.517], 55

     definition [2.515], 55

     derivative of transform [2.521], 55

     inverse [2.519], 55

     of derivative [2.520], 55

     substitution [2.522], 55

     translation [2.524], 55

LAPLACE TRANSFORM PAIRS, 56

LAPLACE TRANSFORM THEOREMS, 55

Laplace transforms, 55

Laplace's formula (surface tension) [3.337], 88

Laplacian

     cylindrical coordinates [2.46], 23

     general coordinates [2.48], 23

     rectangular coordinates [2.45], 23

     spherical coordinates [2.47], 23

LAPLACIAN (SCALAR), 23

lapse rate (adiabatic) [3.294], 84

Larmor frequency [7.265], 157

Larmor radius [7.268], 157

Larmor's formula [7.132], 146

laser

     cavity Q [8.126], 174

     cavity line width [8.127], 174

     cavity modes [8.124], 174

     cavity stability [8.123], 174

     threshold condition [8.129], 174

LASERS, 174

latent heat [5.48], 109

lattice constants of elements, 124

Lattice dynamics, 129

LATTICE FORCES (SIMPLE), 131

lattice plane spacing [6.11], 126

LATTICE THERMAL EXPANSION AND CONDUCTION, 131

lattice vector [6.7], 126

latus-rectum [3.109], 71

Laue equations [6.28], 128

Laurent series [2.169], 31

LCR circuits, 147

LCR DEFINITIONS, 147

least-squares fitting, 60

Legendre equation

     and polynomials [2.422], 47

     definition [2.344], 43

LEGENDRE POLYNOMIALS, 47

Leibniz theorem [2.297], 40

length (dimensions), 17

Lennard-Jones 6-12 potential [6.52], 131

lens blooming [8.7], 162

LENSES AND MIRRORS, 168

lensmaker's formula [8.66], 168

Levi-Civita symbol (3-D) [2.444], 50

l'Hôpital's rule [2.132], 28

LIéNARD-WIECHERT POTENTIALS, 139

light (speed of), 6, 7

LIMITS, 28

line charge (electric field from) [7.29], 138

line fitting, 60

Line radiation, 173

line shape

     collisional [8.114], 173

     Doppler [8.116], 173

     natural [8.112], 173

line width

     collisional/pressure [8.115], 173

     Doppler broadened [8.117], 173

     laser cavity [8.127], 174

     natural [8.113], 173

     Schawlow-Townes [8.128], 174

linear absorption coefficient [5.175], 120

linear expansivity (definition) [5.19], 107

linear expansivity (of a crystal) [6.57], 131

linear regression, 60

linked flux [7.149], 147

liquid drop model [4.172], 103

litre (unit), 5

local civil time [9.4], 177

local sidereal time [9.7], 177

local thermodynamic equilibrium (LTE), 116, 120

ln(1+x) (series expansion) [2.134], 29

logarithm of complex numbers [2.163], 30

logarithmic decrement [3.202], 78

London's formula (interacting dipoles) [6.50], 131

longitudinal elastic modulus [3.241], 81

look-back time (cosmological) [9.94], 184

Lorentz

     broadening [8.112], 173

     constant [6.66], 132

     contraction [3.8], 64

     factor (g) [3.7], 64

     force [7.122], 145

     gauge condition [7.43], 139

LORENTZ (SPACETIME) TRANSFORMATIONS, 64

Lorentz factor (dynamical) [3.69], 68

Lorentz transformation

     in electrodynamics, 141

     of four-vectors, 65

     of momentum and energy, 65

     of time and position, 64

     of velocity, 64

Lorentz-Lorenz formula [7.93], 142

Lorentzian distribution [2.556], 58

Lorentzian (Fourier transform of) [2.506], 54

lumen (unit), 4

luminance [5.168], 119

luminosity distance [9.89], 184

luminosity-magnitude relation [9.31], 179

luminous

     density [5.160], 119

     efficacy [5.169], 119

     efficiency [5.170], 119

     energy [5.157], 119

     exitance [5.162], 119

     flux [5.159], 119

     intensity (dimensions), 17

     intensity [5.166], 119

lux (unit), 4

Mach number [3.315], 86

Mach wedge [3.328], 87

Maclaurin series [2.126], 28

MACROSCOPIC THERMODYNAMIC VARIABLES, 115

Madelung constant (value), 9

Madelung constant [6.55], 131

magnetic

     diffusivity [7.282], 158

     flux quantum, 6, 7

     monopoles (none) [7.52], 140

     permeability, m, m_r[7.107], 143

     quantum number [4.131], 100

     scalar potential [7.7], 136

     susceptibility, c_H, c_B[7.103], 143

     vector potential

         definition [7.40], 139

         from J [7.47], 139

         of a moving charge [7.49], 139

magnetic dipole, see dipole

magnetic field

     around objects, 138

     dimensions, 17

     energy density [7.128], 146

     Lorentz transformation, 141

     static, 136

     strength ( H) [7.100], 143

     thermodynamic work [5.8], 106

     wave equation [7.194], 152

MAGNETIC FIELDS, 138

magnetic flux (dimensions), 17

magnetic flux density (dimensions), 17

magnetic flux density from

     current [7.11], 136

     current density [7.10], 136

     dipole [7.36], 138

     electromagnet [7.38], 138

     line current (Biot-Savart law) [7.9], 136

     solenoid (finite) [7.38], 138

     solenoid (infinite) [7.33], 138

     uniform cylindrical current [7.34], 138

     waveguide [7.190], 151

     wire [7.34], 138

     wire loop [7.37], 138

MAGNETIC MOMENTS, 100

magnetic vector potential (dimensions), 17

MAGNETISATION, 143

magnetisation

     definition [7.97], 143

     dimensions, 17

     isolated spins [4.151], 101

     quantum paramagnetic [4.150], 101

magnetogyric ratio [4.138], 100

MAGNETOHYDRODYNAMICS, 158

magnetosonic waves [7.285], 158

MAGNETOSTATICS, 136

magnification (longitudinal) [8.71], 168

magnification (transverse) [8.70], 168

magnitude (astronomical)

     -flux relation [9.32], 179

     -luminosity relation [9.31], 179

     absolute [9.29], 179

     apparent [9.27], 179

major axis [3.106], 71

Malus's law [8.83], 170

Mars data, 176

mass (dimensions), 17

mass absorption coefficient [5.176], 120

mass ratio (of a rocket) [3.94], 70

MATHEMATICAL CONSTANTS, 9

Mathematics, 19-62

matrices (square), 25

MATRIX ALGEBRA, 24

matrix element (quantum) [4.32], 92

maxima [2.337], 42

MAXWELL'S EQUATIONS, 140

MAXWELL'S EQUATIONS (USING D AND H), 140

MAXWELL'S RELATIONS, 109

Maxwell-Boltzmann distribution

     mean speed [5.86], 112

     most probable speed [5.88], 112

     rms speed [5.87], 112

     speed distribution [5.84], 112

MAXWELL-BOLTZMANN DISTRIBUTION, 112

mean

     arithmetic [2.109], 27

     geometric [2.110], 27

     harmonic [2.111], 27

mean estimator [2.542], 57

mean free path

     and absorption coefficient [5.175], 120

     Maxwell-Boltzmann [5.89], 113

mean intensity [5.172], 120

mean-life (nuclear decay) [4.165], 103

mega, 5

melting points of elements, 124

meniscus [3.339], 88

Mensuration, 35

Mercury data, 176

method of images, 138

metre (unit), 4

metric elements and coordinate systems, 21

MHD equations [7.283], 158

micro, 5

microcanonical ensemble [5.109], 114

micron (unit), 5

microstrip line (impedance) [7.184], 150

Miller-Bravais indices [6.20], 126

milli, 5

minima [2.338], 42

minimum deviation (of a prism) [8.74], 169

minor axis [3.107], 71

minute (unit), 5

mirror formula [8.67], 168

Miscellaneous, 18

mobility (dimensions), 17

mobility (in conductors) [6.88], 134

modal dispersion (optical fibre) [8.79], 169

modified Bessel functions [2.420], 47

modified Julian day number [9.2], 177

modulus (of a complex number) [2.156], 30

MOIRé FRINGES, 35

molar gas constant (dimensions), 17

molar volume, 9

mole (unit), 4

molecular flow [5.99], 113

moment

     electric dipole [7.81], 142

     magnetic dipole [7.94], 143

     magnetic dipole [7.95], 143

moment of area [3.258], 82

moment of inertia

     cone [3.160], 75

     cylinder [3.155], 75

     dimensions, 17

     disk [3.168], 75

     ellipsoid [3.163], 75

     elliptical lamina [3.166], 75

     rectangular cuboid [3.158], 75

     sphere [3.152], 75

     spherical shell [3.153], 75

     thin rod [3.150], 75

     triangular plate [3.169], 75

     two-body system [3.83], 69

moment of inertia ellipsoid [3.147], 74

MOMENT OF INERTIA TENSOR, 74

moment of inertia tensor [3.136], 74

MOMENTS OF INERTIA, 75

momentum

     definition [3.64], 68

     dimensions, 17

     generalised [3.218], 79

     relativistic [3.70], 68

MOMENTUM AND ENERGY TRANSFORMATIONS, 65

MONATOMIC GAS, 112

monatomic gas

     entropy [5.83], 112

     equation of state [5.78], 112

     heat capacity [5.82], 112

     internal energy [5.79], 112

     pressure [5.77], 112

monoclinic system (crystallographic), 127

MOON DATA, 176

motif [6.31], 128

motion under constant acceleration, 68

Mott scattering formula [4.180], 104

m, m_r (magnetic permeability) [7.107], 143

multilayer films (in optics) [8.8], 162

multimode dispersion (optical fibre) [8.79], 169

multiplicity (quantum)

     j [4.133], 100

     l [4.112], 98

multistage rocket [3.95], 70

MULTIVARIATE NORMAL DISTRIBUTION, 58

MUON CONSTANTS, 9

mutual

     capacitance [7.134], 146

     inductance (definition) [7.147], 147

     inductance (energy) [7.135], 146

mutual coherence function [8.97], 172

nabla, 21

NAMED INTEGRALS, 45

nano, 5

natural broadening profile [8.112], 173

natural line width [8.113], 173

Navier-Stokes equation [3.301], 85

nearest neighbour distances, 127

Neptune data, 176

neutron

     Compton wavelength, 8

     magnetic moment, 8

     mass, 8

     molar mass, 8

NEUTRON CONSTANTS, 8

neutron star degeneracy pressure [9.77], 183

newton (unit), 4

Newton's law of Gravitation [3.40], 66

Newton's lens formula [8.65], 168

NEWTON'S RINGS, 162

Newton's rings [8.1], 162

Newton-Raphson method [2.594], 61

NEWTONIAN GRAVITATION, 66

noggin, 13

NOISE, 117

noise

     figure [5.143], 117

     Johnson [5.141], 117

     Nyquist's theorem [5.140], 117

     shot [5.142], 117

     temperature [5.140], 117

normal (unit principal) [2.285], 39

normal distribution [2.553], 58

normal plane, 39

NUCLEAR BINDING ENERGY, 103

NUCLEAR COLLISIONS, 104

NUCLEAR DECAY, 103

nuclear decay law [4.163], 103

nuclear magneton, 7

number density (dimensions), 17

numerical aperture (optical fibre) [8.78], 169

NUMERICAL DIFFERENTIATION, 61

NUMERICAL INTEGRATION, 61

Numerical methods, 60

NUMERICAL SOLUTIONS TO f(x) = 0, 61

NUMERICAL SOLUTIONS TO ORDINARY DIFFERENTIAL EQUATIONS, 62

nutation [3.194], 77

Nyquist's theorem [5.140], 117

OBLIQUE ELASTIC COLLISIONS, 73

obliquity factor (diffraction) [8.46], 166

obliquity of the ecliptic [9.13], 178

observable (quantum physics) [4.5], 90

Observational astrophysics, 179

OBSERVATIONAL COSMOLOGY, 184

octahedron, 38

odd functions, 53

ODEs (numerical solutions), 62

ohm (unit), 4

Ohm's law (in MHD) [7.281], 158

Ohm's law [7.140], 147

opacity [5.176], 120

open-wire transmission line [7.182], 150

operator

     angular momentum

         and other operators [4.23], 91

         definitions [4.105], 98

     Hamiltonian [4.21], 91

     kinetic energy [4.20], 91

     momentum [4.19], 91

     parity [4.24], 91

     position [4.18], 91

     time dependence [4.27], 91

OPERATORS, 91

optic branch (phonon) [6.37], 129

optical coating [8.8], 162

optical depth [5.177], 120

OPTICAL FIBRES, 169

optical path length [8.63], 168

Optics, 161-174

ORBITAL ANGULAR DEPENDENCE, 97

ORBITAL ANGULAR MOMENTUM, 98

orbital motion, 71

orbital radius (Bohr atom) [4.73], 95

order (in diffraction) [8.26], 164

ordinary modes [7.271], 157