Basic function of plane waves Ψ(x,t)
Ψ(x,t) = Aexp( i(kx-ωt) )
Wavelength to wave number relation
k = 2π/λ
DeBroglie relation
λ = h/p
Momentum to wave number relation
k = (1/ħ) p
Reduced planck
ħ = h/2π
Planck law (photon energy)
E = hν (v is frequency)
Angular frequency from freq.
ω = 2πν
Non-relativistic kinetic energy from momentum
p²/2m = E
Non-relativistic kinetic energy from momentum in terms of planck
(ħ² k²) / 2m = ħω
Uncertainty principle
ΔxΔp ≥ ħ/2