Equations

Question 1

Momentum

Answer 1

p=hbark

Question 2

Energy of free electron

Answer 2

E=hbar^2k^2/2m

Question 3

Schrodinger eqn

Answer 3

H|ψ>=E|Ψ>, H|C>=E|C>

Question 4

Momentum operator

Answer 4

P=-ihar*laplacian

Question 5

Hamiltonian

Answer 5

H=1/2mP(operator)^2+V=-habr^2/2m*Δ^2+V

Question 6

Hamiltonian matrix elements

Answer 6

=<Hi|H|Hj>

Question 7

2nd order perturbation theory

Answer 7

E = E0+<ψn|H|ψn>+Σn’≠n<ψn|Hpert|ψn’>/εn-εn’

Question 8

LCAO for diatomic molecule

Answer 8

(E1 0 0 E2)(C1 C2) = E (1 S S 1) (C1 C2)

Question 9

Energy for LCAO when E1=E2=E0

Answer 9

E = Eo±|U|

Question 10

(C1 C2) when E1=E2

Answer 10

1/root(2)*(1 ±1)

Question 11

E for LCAO when E1≠E2

Answer 11

E=Eav±root(Ecov^2+Eionic^2)

Question 12

Ecov

Answer 12

Ecov=2|U|

Question 13

Eionic

Answer 13

=|E1-E2/2|

Question 14

Eav

Answer 14

=E1+E2/2

Question 15

Bloch Theorem

Answer 15

ψ(r+a) = exp(ikr)ψ(r)

Question 16

Bloch function

Answer 16

ψn(r)=exp(ikr)un(r)

Question 17

average p

Answer 17

<p>=<ψnk|P|ψnk> = hbark + <Un|p|Un> = Pcrystal ( + Pnn atomic part which =0 when definite parity)
</p>

Question 18

Effective mass

Answer 18

1/m*=1/hbar^2d^2E/Dk^2=1/m(1+Ep/Eg)

Question 19

Ep (energy of kane momentum)

Answer 19

Ep=2Pcv^2/m

Question 20

Energy of dipole in magnetic field

Answer 20

Hso proportional σΔV*P

Question 21

Vg Group velocity

Answer 21

Vg=dω/dk=1/hbarΔE

Question 22

acceleration with group velocity

Answer 22

a = dVg/dt=M^-1*F

Question 23

M^-1

Answer 23

M^-1=1/hbar^dE/dkidkj

Question 24

Important Lattice Points

Answer 24

L = 1/2[111]2π/a
Γ = [000]
X = [100]2π/α

Question 25

Bowing

Answer 25

E(x) = EA(1-x)+EBx+bx(1-x)

Question 26

State radius

Answer 26

an=a0n^2

Question 27

binding energy

Answer 27

En=-Er/n^2

Question 28

Number of states per unit volume

Answer 28

g(E)dE=g(k)dK

Question 29

3D density of states

Answer 29

g(E) proportional m*^3/2E^1/2

Question 30

2D density of states

Answer 30

g(E) proportional m*E^0

Question 31

1D density of states

Answer 31

g(E) proportional m*^1/2E^-1/2

Question 32

boltzmann occupation function

Answer 32

fB(E) proportional exp(-E/kT)

Question 33

Fermi occupation function

Answer 33

f(E) = 1/(1+exp((E-Ef)/kt)

Question 34

Number of electrons per unit volume

Answer 34

n=Nc*exp((Ef-Ec)/kt)

Question 35

Nc

Answer 35

Nc=2(me*kT/2πhbar^2)^3/2

Question 36

Number of holes per unit volume

Answer 36

p = Nv*exp((Ev-Ef)/kT)

Question 37

Law of mass action

Answer 37

np=ni^2=NcNv*exp(-Eg/kT)

Question 38

Fermis golden rule for number of excitations per unit vol

Answer 38

Rcv = 2π/hbar|<c|Hopt|v>/2|^2*gcv(e)

Question 39

Reduced Mass

Answer 39

1/μ = 1/mc+1/mv (replace m* with μ in DOS formulas for joint density of states)

Question 40

Intensity

Answer 40

I = F^2/2Z0 = hbarωφ

Question 41

wavelength in terms of k

Answer 41

λ= 2π/k=2πc/ω=hc/E

Question 42

current density

Answer 42

J = σε

Question 43

Drift velocity

Answer 43

vd= με (μ = mobility)

Question 44

mobility

Answer 44

μ = qτ/μ*

Question 45

conductivity

Answer 45

σ= 1/ρ = neμ = nq^2τ/m*

Question 46

Lorentz Force

Answer 46

F = q(ε+vg x B)

Question 47

Hall Resistance

Answer 47

Rh=1/nq

Question 48

cyclotron frequency

Answer 48

ωc = qB/m*

Question 49

Landau level energy

Answer 49

Ε = hbar^2kz^2/2m+(l+1/2)hbarωψ

Question 50

Lattice Scattering

Answer 50

μl proportional T^-3/2

Question 51

impurity scattering

Answer 51

μi proportional T^3/2

Question 52

1/total scattering

Answer 52

1/μ = 1/μl+1/μi

Question 53

potential

Answer 53

dφ(x)/dx = ε(x)

Question 54

Gauss’ law for charge density in 1D

Answer 54

dε(x)/dx = 1/ε*ρ(x)

Question 55

Electric field

Answer 55

ε = F/d = V/d (uniform) = Q/4πε0r^2 (radial)

Question 56

Magnetic field

Answer 56

B = μ0I/2πr

Question 57

Magnetic force

Answer 57

F = qvBsin(90) = m*v^2/r (centripetal force)