Order 1238142: Condensed matter

99/99 NOVEMBER 19xx Page 1 of ??

CONDENSED MATTER PHYSICS FORMULA SHEET

vt =

√ 3kBT

m

v = −eEτ me

j = ne2τ

me E = σE = E

ρ σ = nμe

μ = eτ

me

EH = RHjxBz wEH = eBzvx

RH = EH jxBz

= −1 ne

κ = 1

3 ncv〈v〉λ

κ

σ = constant = LT

L = 3

2

( kB e

)2 jq = Πj

jq = 1

3 (cvT)nv

S = Π

T =

−kB 2e

E(k) = �

2k2

2me

k = (kx,ky,kz) = ( nx2π

L , ny2π

L , nz2π

L )

ψ(r) = 1√ V eik.r

EF = �

2

2me (3π2n)2/3

TF = EF kB

kF = (3π 2n)1/3 = (

3π2N

V )1/3

99/99 NOVEMBER 19xx Page 2 of ??

vF = √

2EF /me = �kF /me

g(E)dE = dN

dE dE =

V

2π2

( 2me �2

)3/2 E1/2dE

CV = π2

3 k2BTg(E) =

π2

3

( 3NkB

2

) ( T

TF

)

L = π2

3

( kB e

)2

APF = atomic packing factor = volume of atoms in unit cell

volume of unit cell

R = ma1 + na2 + oa3

G = m′b1 + n ′b2 + o

′b3

R.G = 2π, eiG.R = 1, eiG.(r+R) = eiG.r

ai.bj = 2πδij

b1 = 2π a2 × a3

a1.(a2 × a3) , b2 = 2π

a3 × a1 a1.(a2 × a3)

, b3 = 2π a1 × a2

a1.(a2 × a3) ,

1

d2 hkl = h2 + k2 + l2

a2

S(k) = ∑

atoms j in unit cell

fje 2πi(hxj +kyj +lzj )

nλ = 2dsinΘ

ψq(r) = e iq.ruqr

uq(r) = uq(r + R)

vn(k) = dEn(k)

�dk( 1

m∗ ij

) =

1

�2

( ∂2E

∂ki∂kj

) i,j = x,y,z

E = �0 − 2tcos(ka)

v =

√ B

ρ

ω = 2 √ κm|sin(ka

2 )|

99/99 NOVEMBER 19xx Page 3 of ??

k = 2π

aN m = 2π/λ

En = (n + 1

2 )�ω

En = − mee

4

8�20h 2

1

n2

nintrinsic = pintrinsic = √ np =

1√ 2 ( kBT

π�2 )3/2(m∗em

∗ h)

3/4e−Egap/2kB T

μ = 1

2 (�c + �v) +

3

4 (kBT)log

( m∗h m∗e

)3/4

M = φH, μ = μ0(1 + χ), μr = 1 + χ

χLarmor = − Zne2μ0〈r2〉

6m

χLandau = − 1

3 χPauli, χPauli = μ0μ

2 Bg(EF )

χCurie/Langevin = nμ0(gμB)

2

3

J(J + 1)

kBT = C

T