The Cambridge Handbook of Physics
Formulas
Index from 'orthogonal matrix' to 'Sakur-Tetrode equation'
orthogonal matrix [2.85], 25
orthogonality
associated Legendre functions [2.435],
48
Legendre polynomials [2.425], 47
orthorhombic system (crystallographic), 127
Oscillating systems, 78
osculating plane, 39
Otto cycle efficiency [5.13], 107
overdamping [3.201], 78
p orbitals [4.95], 97
P-waves [3.263], 82
packing fraction (of spheres), 127
paired strip (impedance of) [7.183], 150
parabola, 38
parabolic motion [3.88], 69
parallax (astronomical) [9.46], 180
parallel axis theorem [3.140], 74
parallel impedances [7.158], 148
parallel wire feeder (inductance) [7.25], 137
paramagnetic susceptibility (Pauli) [6.79], 133
paramagnetism (quantum), 101
PARAMAGNETISM AND DIAMAGNETISM, 144
parity operator [4.24], 91
Parseval's relation [2.496], 53
Parseval's theorem
integral form [2.497], 53
series form [2.481], 52
PARTIAL DERIVATIVES, 42
partial widths (and total width) [4.176], 104
PARTICLE IN A RECTANGULAR BOX, 94
Particle motion, 68
partition function
atomic [5.126], 116
definition [5.110], 114
macroscopic variables from, 115
pascal (unit), 4
PAULI MATRICES, 26
Pauli matrices [2.94], 26
Pauli paramagnetic susceptibility [6.79], 133
Pauli spin matrices (and Weyl eqn.) [4.182], 104
Pearson's r [2.547], 57
Peltier effect [6.82], 133
pendulum
compound [3.182], 76
conical [3.180], 76
double [3.183], 76
simple [3.179], 76
torsional [3.181], 76
PENDULUMS, 76
perfect gas, 110
pericentre (of an orbit) [3.110], 71
perimeter
of circle [2.262], 37
of ellipse [2.267], 37
PERIMETER, AREA AND VOLUME, 37
period (of an orbit) [3.113], 71
Periodic table, 124
permeability
dimensions, 17
magnetic [7.107], 143
of vacuum, 6, 7
permittivity
dimensions, 17
electrical [7.90], 142
of vacuum, 6, 7
permutation tensor (eijk)
[2.444],
50
perpendicular axis theorem [3.148], 74
Perturbation theory, 102
peta, 5
petrol engine efficiency [5.13], 107
phase (of an orbit) [3.112], 71
phase object (diffraction by weak) [8.43], 165
phase rule (Gibbs's) [5.54], 109
phase speed (wave) [3.325], 87
PHASE TRANSITIONS, 109
PHONON DISPERSION RELATIONS, 129
phonon modes (mean energy) [6.40], 130
PHOTOMETRIC WAVELENGTHS, 179
PHOTOMETRY, 119
photon energy [4.3], 90
Physical constants, 6
PI ( p) TO 1000 DECIMAL PLACES, 18
Pi (p), 9
pico, 5
pipe (flow of fluid along) [3.305], 85
pipe (twisting of) [3.255], 81
pitch angle, 159
Planck
constant, 6, 7
constant (dimensions), 17
function [5.184], 121
length, 7
mass, 7
time, 7
Planck-Einstein relation [4.3], 90
plane polarisation, 170
PLANE TRIANGLES, 36
plane wave expansion [2.428], 47
PLANETARY BODIES, 180
PLANETARY DATA, 176
plasma
beta [7.278], 158
dispersion relation [7.261], 157
frequency [7.259], 157
group velocity [7.264], 157
phase velocity [7.262], 157
refractive index [7.260], 157
Plasma physics, 156
PLATONIC SOLIDS, 38
Pluto data, 176
p-n junction [6.92], 134
Poincaré sphere, 171
point charge (electric field from) [7.5], 136
Poiseuille flow [3.305], 85
Poisson brackets [3.224], 79
Poisson distribution [2.550], 57
Poisson ratio
and elastic constants [3.251], 81
simple definition [3.231], 80
Poisson's equation [7.3], 136
polarisability [7.91], 142
Polarisation, 170
POLARISATION, 142
polarisation (electrical, per unit volume) [7.83], 142
polarisation (of radiation)
angle [8.81], 170
axial ratio [8.88], 171
degree of [8.96], 171
elliptical [8.80], 170
ellipticity [8.82], 170
reflection law [7.218], 154
polarisers [8.85], 170
polhode, 63, 77
POPULATION DENSITIES, 116
potential
chemical [5.28], 108
difference (and work) [5.9], 106
difference (between points) [7.2], 136
electrical [7.46], 139
electrostatic [7.1], 136
energy (elastic) [3.235], 80
energy in Hamiltonian [3.222], 79
energy in Lagrangian [3.216], 79
field equations [7.45], 139
four-vector [7.77], 141
grand [5.37], 108
Liénard-Wiechert, 139
Lorentz transformation [7.75], 141
magnetic scalar [7.7], 136
magnetic vector [7.40], 139
Rutherford scattering [3.114], 72
thermodynamic [5.35], 108
velocity [3.296], 84
POTENTIAL FLOW, 84
POTENTIAL STEP, 92
POTENTIAL WELL, 93
power (dimensions), 17
power gain
antenna [7.211], 153
short dipole [7.213], 153
POWER SERIES, 28
Power theorem [2.496], 53
Poynting vector (dimensions), 17
Poynting vector [7.130], 146
pp (proton-proton) chain, 182
Prandtl number [3.314], 86
precession (gyroscopic) [3.191], 77
PRECESSION OF EQUINOXES, 178
pressure
broadening [8.115], 173
critical [5.75], 111
degeneracy [9.77], 183
dimensions, 17
fluctuations [5.136], 116
from partition function [5.118], 115
hydrostatic [3.238], 80
in a monatomic gas [5.77], 112
radiation, 152
thermodynamic work [5.5], 106
waves [3.263], 82
primitive cell [6.1], 126
primitive vectors (and lattice vectors) [6.7], 126
primitive vectors (of cubic lattices), 127
PRINCIPAL AXES, 74
principal moments of inertia [3.143], 74
principal quantum number [4.71], 95
principle of least action [3.213], 79
prism
determining refractive index [8.75],
169
deviation [8.73], 169
dispersion [8.76], 169
minimum deviation [8.74], 169
transmission angle [8.72], 169
PRISMS (DISPERSING), 169
probability
conditional [2.568], 59
density current [4.13], 90
distributions
continuous, 58
discrete, 57
joint [2.569], 59
Probability and statistics, 57
product (derivative of) [2.294], 40
product (integral of) [2.355], 44
product of inertia [3.136], 74
progression (arithmetic) [2.105], 27
progression (geometric) [2.108], 27
PROGRESSIONS AND SUMMATIONS, 27
projectiles, 69
propagation in cold plasmas, 157
PROPAGATION IN CONDUCTING MEDIA, 155
PROPAGATION OF ELASTIC WAVES, 83
PROPAGATION OF LIGHT, 65
PROTON CONSTANTS, 8
proton mass, 6
proton-proton chain, 182
pulsar
braking index [9.66], 182
characteristic age [9.67], 182
dispersion [9.72], 182
magnetic dipole radiation [9.69], 182
PULSARS, 182
pyramid (centre of mass) [3.175], 76
pyramid (volume) [2.273], 37
Q, see quality factor
Q (Stokes parameter) [8.90], 171
QUADRATIC EQUATIONS, 50
quadrature, 44, 61
quality factor
Fabry-Perot etalon [8.14], 163
forced harmonic oscillator [3.211], 78
free harmonic oscillator [3.203], 78
laser cavity [8.126], 174
LCR circuits [7.152], 148
quantum concentration [5.83], 112
Quantum definitions, 90
QUANTUM PARAMAGNETISM, 101
Quantum physics, 89-104
QUANTUM UNCERTAINTY RELATIONS, 90
quarter-wave condition [8.3], 162
quarter-wave plate [8.85], 170
quartic minimum [2.339], 42
RADIAL FORMS, 22
radian (unit), 4
radiance [5.156], 118
radiant
energy [5.145], 118
energy density [5.148], 118
exitance [5.150], 118
flux [5.147], 118
intensity (dimensions), 17
intensity [5.154], 118
radiation
blackbody [5.184], 121
bremsstrahlung [7.297], 160
Cherenkov [7.247], 156
field of a dipole [7.207], 153
flux from dipole [7.131], 146
resistance [7.209], 153
synchrotron [7.287], 159
RADIATION PRESSURE, 152
radiation pressure
extended source [7.203], 152
isotropic [7.200], 152
momentum density [7.199], 152
point source [7.204], 152
specular reflection [7.202], 152
Radiation processes, 118
RADIATIVE TRANSFER, 120
radiative transfer equation [5.179], 120
radiative transport (in stars) [9.63], 181
radioactivity, 103
RADIOMETRY, 118
radius of curvature
definition [2.283], 39
in bending [3.258], 82
relation to curvature [2.288], 39
radius of gyration (see footnote), 75
Ramsauer effect [4.52], 93
RANDOM WALK, 59
random walk
Brownian motion [5.98], 113
one-dimensional [2.563], 59
three-dimensional [2.565], 59
range (of projectile) [3.90], 69
Rankine conversion [1.3], 15
Rankine-Hugoniot shock relations [3.334], 87
Rayleigh distribution [2.555], 58
Rayleigh resolution criterion [8.41], 165
Rayleigh scattering [7.236], 155
Rayleigh's theorem [2.497], 53
Rayleigh-Jeans law [5.187], 121
reactance (definition), 148
reciprocal
lattice vector [6.8], 126
matrix [2.83], 25
vectors [2.16], 20
reciprocity [2.331], 42
RECOGNISED NON-SI UNITS, 5
rectangular aperture diffraction [8.39], 165
rectangular coordinates, 21
rectangular cuboid moment of inertia [3.158], 75
rectifying plane, 39
recurrence relation
associated Legendre functions [2.434],
48
Legendre polynomials [2.424], 47
redshift
-angular diameter relation [9.92], 184
-distance relation [9.89], 184
-flux density relation [9.90], 184
-time relation [9.94], 184
cosmological [9.87], 184
gravitational [9.74], 183
REDUCED MASS (OF TWO INTERACTING BODIES), 69
reduced units (thermodynamics) [5.71], 111
reflectance coefficient
and Fresnel equations [7.227], 154
dielectric film [8.4], 162
dielectric multilayer [8.8], 162
reflection coefficient
acoustic [3.283], 83
dielectric boundary [7.230], 154
potential barrier [4.58], 94
potential step [4.41], 92
potential well [4.48], 93
transmission line [7.179], 150
reflection grating [8.29], 164
reflection law [7.216], 154
REFLECTION, REFRACTION AND TRANSMISSION, 154
refraction law (Snell's) [7.217], 154
refractive index of
dielectric medium [7.195], 152
ohmic conductor [7.234], 155
plasma [7.260], 157
refrigerator efficiency [5.11], 107
regression (linear), 60
relativistic beaming [3.25], 65
relativistic doppler effect [3.22], 65
RELATIVISTIC DYNAMICS, 68
RELATIVISTIC ELECTRODYNAMICS, 141
RELATIVISTIC WAVE EQUATIONS, 104
relativity (general), 67
relativity (special), 64
relaxation time
and electron drift [6.61], 132
in a conductor [7.156], 148
in plasmas, 156
residuals [2.573], 60
Residue theorem [2.171], 31
residues (in complex analysis), 31
resistance
and impedance, 148
dimensions, 17
energy dissipated in [7.155], 148
radiation [7.209], 153
resistivity [7.142], 147
resistor, see resistance
resolving power
chromatic (of an etalon) [8.21], 163
of a diffraction grating [8.30], 164
Rayleigh resolution criterion [8.41],
165
resonance
forced oscillator [3.209], 78
resonance lifetime [4.177], 104
resonant frequency (LCR) [7.150], 148
RESONANT LCR CIRCUITS, 148
restitution (coefficient of) [3.127], 73
retarded time, 139
revolution (volume and surface of), 39
Reynolds number [3.311], 86
ribbon (twisting of) [3.256], 81
Ricci tensor [3.57], 67
Riemann tensor [3.50], 67
right ascension [9.8], 177
rigid body
angular momentum [3.141], 74
kinetic energy [3.142], 74
Rigid body dynamics, 74
rigidity modulus [3.249], 81
ripples [3.321], 86
rms (standard deviation) [2.544], 57
Robertson-Walker metric [9.95], 185
Roche limit [9.43], 180
rocket equation [3.94], 70
ROCKETRY, 70
rod
bending, 82
moment of inertia [3.150], 75
stretching [3.230], 80
waves in [3.271], 82
Rodrigues' formula [2.423], 47
Roots of quadratic and cubic equations, 50
Rossby number [3.316], 86
rot (curl), 22
ROTATING FRAMES, 66
ROTATION MATRICES, 26
rotation measure [7.273], 157
Runge Kutta method [2.604], 62
RUTHERFORD SCATTERING, 72
Rutherford scattering formula [3.124], 72
Rydberg constant, 6, 7
and Bohr atom [4.77], 95
dimensions, 17
Rydberg's formula [4.78], 95
s orbitals [4.92], 97
S-waves [3.262], 82
Sackur-Tetrode equation [5.83], 112