Useful constants

  1. Electron charge: e =1.602 × 10-19 C
  2. Electron mass: me = 9.110 × 10-31 kg
  3. Planck's constant divided by (2p): ħ = 1.05459 × 10-34 J × s ↔ h = 6.63 × 10-34 J × s
  4. Avogardro number, N = 6.022 × 1023 /mol
  5. Boltzmann's constant,  k = 1.380658 × 10-23 J/K = 8.617 × 10-5 eV/K

 

Energy conversion factors

 

  1. 1 eV  =  2.41797 × 1014 Hz = 8065.48 cm-1 = 1239.85 nm = 1.16045 × 104 K
  2. 1 a.u =  27.211396 eV 
  3. 1 degree Kelvin = 0.0862  meV = 0.695 cm-1
  4. 1 GHz = 6.6 × 10-7 eV         (energy units by laser physicists)

(f = 6.58 × 1015 or ω = 4.13 × 1016 Hz « E = 27.21 eV)

  1. photon momentum   k= 2.7 ´ 10-4 E (eV)

 

Atomic units  

  1. length, a0 = 0.528 Å
  2. time, a0/v0 = 24.2 asec  (1 fs = 41 au)
  3. frequency, f = v0/(2πa0) = 6.58 × 1015 s-1
  4. angular frequency, ω = v0/(a0) = 4.13 ´ 1016 sec-1
  5. momentum, p0 = mvo = 1.993 × 10-24 kg m s-1
  6. electric field, E = 5.14 ´ 109 V/cm
  7. magnetic field, B = 2.35 ´ 105 tesla
  8. intensity, I = 3.51 ´ 1016 W/cm2

 

Lasers

1.      UP = E2/4= 9.33 × 10-14 I (1014 W/cm2)(0.8m) = 6 eV

2.      Keldysh parameter

3.      time-frequency width relation:

4.      Gaussian pulse  

1)             

2)        width in eV for a Gaussian pulse with   is 1.83 eV

Short hand notations

1024  yotta(Y);  1021  zetta(Z); 1018  exa(E); 1015  peta(P); 1012  tera(T); 109  giga(G); 106  mega(M); 103  kilo(k); 102  hecto(h); 101  deka(da)

10-24  yocto(y); 10-21  zepto(z); 10-18  atto(a); 10-15  femto(f); 10-12  pico(p); 10-9  nano(n); 10-6  micro(µ); 10-3  milli(m); ; 10-2  centi(c); 10-1  deci(d)