528
J Gaussian, S.I., and Atomic Units
J.2 Maxwell’s Equations in S.I. Units
In S.I. units, Maxwell’s equations in a vacuum are (Jackson 1975)
Gauss’s laws :
∇·E =
ρ
0
, ∇·B = 0
Ampere’s law :
∇×B −
1
c 2
∂E
∂t
= μ 0 J Q ,
Faraday’s law :
∇×E +
∂B
∂t
= 0
Lorentz force;
F = Q (E + v×B)
(J.4)
where E is the electric field, B is the magnetic field,
The permittivity is 0 = 8.85434 × 10 −12 C 2 /N · m 2 .
The permeability is μ 0 = 4π × 10 −7 m·kg/A
2
·s 2 .
The speed of light is c = 1/
√ 0 μ 0 = 2.99792458×10 8 m/s
J.2.1 Conversion Between S.I. Units and Atomic Units
Below let κ 0 = 1/(4ππ 0 ).
Angular momentum= ¯
h=1au=1.05457 × 10 −34 J · s.
Charge =electron charge=e=1au=1.60218 × 10 −19 C.
Mass=mass of electron=m e =1 au=9.10940 × 10 −31 kg.
Length=radius of first Bohr orbit=a B =1 au= ¯
h 2 /κ 0 me 2 = 5.2917 × 10 −11 m.
Energy=E 0 = κ 2
0 me 4 / ¯
h 2 = 1 au=4.3597 × 10 −18 J.
Velocity=v B = κ 0 e 2 / ¯
h=1 au=2.1877 × 10 6 m/s.
Momentum=p B = mv B = κ 0 me 2 / ¯
h =1 au=1.9928 × 10 −24 kg·m/s.
Time=t B = a B /v B = ¯
h 3 /κ 2
0 me 4 =1 au=2.4189 × 10 −17 s.
Frequency=f B = v B /a B = κ 2
0 me 4 / ¯
h 3 =1 au=4.1341 × 10 16 s −1 .
Force=F B = κ 0 e/a 2
B =1 au=5.1422 × 10 11 V/m.
References
Jackson JD (1975) Classical electrodynamics. Wiley, New York
Bethe HA, Salpeter EE (1957) Quantum mechanics oif one and two electron atoms. Academic
Press, New York
J Gaussian, S.I., and Atomic Units
J.2 Maxwell’s Equations in S.I. Units
In S.I. units, Maxwell’s equations in a vacuum are (Jackson 1975)
Gauss’s laws :
∇·E =
ρ
0
, ∇·B = 0
Ampere’s law :
∇×B −
1
c 2
∂E
∂t
= μ 0 J Q ,
Faraday’s law :
∇×E +
∂B
∂t
= 0
Lorentz force;
F = Q (E + v×B)
(J.4)
where E is the electric field, B is the magnetic field,
The permittivity is 0 = 8.85434 × 10 −12 C 2 /N · m 2 .
The permeability is μ 0 = 4π × 10 −7 m·kg/A
2
·s 2 .
The speed of light is c = 1/
√ 0 μ 0 = 2.99792458×10 8 m/s
J.2.1 Conversion Between S.I. Units and Atomic Units
Below let κ 0 = 1/(4ππ 0 ).
Angular momentum= ¯
h=1au=1.05457 × 10 −34 J · s.
Charge =electron charge=e=1au=1.60218 × 10 −19 C.
Mass=mass of electron=m e =1 au=9.10940 × 10 −31 kg.
Length=radius of first Bohr orbit=a B =1 au= ¯
h 2 /κ 0 me 2 = 5.2917 × 10 −11 m.
Energy=E 0 = κ 2
0 me 4 / ¯
h 2 = 1 au=4.3597 × 10 −18 J.
Velocity=v B = κ 0 e 2 / ¯
h=1 au=2.1877 × 10 6 m/s.
Momentum=p B = mv B = κ 0 me 2 / ¯
h =1 au=1.9928 × 10 −24 kg·m/s.
Time=t B = a B /v B = ¯
h 3 /κ 2
0 me 4 =1 au=2.4189 × 10 −17 s.
Frequency=f B = v B /a B = κ 2
0 me 4 / ¯
h 3 =1 au=4.1341 × 10 16 s −1 .
Force=F B = κ 0 e/a 2
B =1 au=5.1422 × 10 11 V/m.
References
Jackson JD (1975) Classical electrodynamics. Wiley, New York
Bethe HA, Salpeter EE (1957) Quantum mechanics oif one and two electron atoms. Academic
Press, New York