(Ek , θ) to k conversion in ARPES. (k is in [Å-1], Ek is in [eV], theta is 0 at normal.)
k// = 0.512 (√Ek ) )[eV] sin θ. ∵Ek = ( ℏ 2 /2m ) k2 , k = √(2m/ ℏ2) √Ek
The E- k parabola with the effective mass m* =α m0 (k is in [Å-1], Ek is in [eV]).
E = ( 3.81 /α) k//2
1240 / hv [eV] = λ [nm]. ∵ E = hc/λ[J]
= hc/eλ[eV]
With λ in nm, E = hc×10^9/eλ
because h = 6.626*10^-34[J・s]
e = 1.602*10^-19[C]
c = 2.998*10^8[m/s],
E≒1240/λ[eV]
(The direct answer using above numerical values is 1.23999675405742822E3.
Thus the value 1240 has a fairly good accuracy.)
ν [Hz] = 3 *10^17 / λ [nm] ∵ v [Hz] = c /λ = 2.998*10^8[m/s]*10^9 / λ[in nm]
The Frequency of the 532nm laser is 563909774436090.226Hz ≒ 5.64 *10^14 [Hz] = 564 [PHz].
The spectral line width of 0.00001nm for the 532nm laser corresponds to
Δν = 3 *10^17 / 532.0 - 3 *10^17 / 532.00001
= 10599807.5909121994
≒ 11 MHz.
1 [THz] = 4.14 [meV] ∵ v [Hz] = c /λ = 2.998*10^8[m/s]*10^9 / λ[nm]
= 2.998*10^8[m/s] *10^9/ (1240/E[eV])
= 2.998 *10^17 *E[eV] / 1240
=2.417*10^14*E[eV]
E[eV] = 4.14 +10^-15 v [Hz]
v=1*10^12 [Hz] -> E[eV]=4.14 *10^-3[eV]
1 [cm-1 ] = 1.23984×10-4 [eV]
1 [eV] = 1.23984*10^-4 k [cm-1]