Constants
Planck constant
Boltzmann constant
Electron mass
Elektron charge
Proton mass
Speed of light
Electric constant
Magnetic constant
Bohr radius
Bohr magneton
g-factor electron
Avogadro constant
h
h̄ = h/2π
kB
me
−e
mp
c
ε0
µ0
a0
µB
ge
NA
6.62 10−34 Js
1.05 10−34 Js
1.38 10−23 J/K
9.11 10−31 kg
−1.6 10−19 C
1.67 10−27 kg
3.00 108 m/s
8.85 10−12 C/(Vm)
4π 10−7 Vs/(Am)
0.529 10−10 m
9.274 10−24 J
2.0023
6.022 1023 1/mol
Formula
De-Broglie
λ=
h
; p~ = h̄~k
|~p|
1
2m
|~p|2 =
h̄2
2m
2
~ k kinetic energy of free particles
E=
reciprocal lattice vectors
~b1 = 2π ~a2 × ~a3
~a1 (~a2 × ~a3 )
~b2 = 2π ~a3 × ~a1
~a1 (~a2 × ~a3 )
~b3 = 2π ~a1 × ~a2
~a1 (~a2 × ~a3 )
Distance of planes
Condition for elastic scattering
Deflection angle
Debye wave vector
Debye frequency and temperature
Thermal energy Debye model
2π
~ min G
d = ~ ~k
G
θ
sin( ) = − ~ ~k 2
G
√
3
kD = 6π 2 n
ωD = vS kD , TD = h̄ωD /kB
Eth = 9N kB T (
T 3 Z TD /T x3
)
dx
TD
ex − 1
0
s
Dispersion linear chain
Group and phase velocity
~ ; ~k = ~k 0 ∆~k = G
4D ka ω(k) =
sin(
)
m 2 dω
ω
vg =
, vph =
dk
k
Fermi-Dirac distribution
f (E) =
1
exp( E−µ
)
kB T
Fermi wave vector
√
3
kF = 3π 2 n
Fermi energy
EF =
Density of states free electron gas
D(E) =
+1
h̄2 2
k
2m F
3 Ne √
2 EF3/2
E
Dielectric function Drude model
ω2
ε(ω) = 1 − 2 p
, ωp =
ω + iω/τ
Mass action law for semiconductors
np = 4
Magnetization paramagnetic material
BCS temperature
kB T 3
2
2πh̄
M = nµAt L(
s
e2 n
0 m
(m∗e m∗h )3/2 e−Eg /kB T
µAt B
1
), L(x) = coth(x) −
kB T
x
Tc = 1.14 TD exp(−
1
)
u D(EF )