Final answer:
The relation between the real parameters h, k, and w in the context of an electromagnetic wave is that the reduced Planck's constant ħ is h/2π, the wave vector k equates to 2π/λ, and the angular frequency w is 2πf. Furthermore, for electromagnetic waves in a vacuum, the relation w = ck holds, showing direct proportionality between angular frequency and wave number.
Step-by-step explanation:
In the equation provided, E = ï E₀ exp[i(hz wt) - xx], the term exp[i(hz wt) - xx] suggests a wave propagating in space with certain wave characteristics. In the context of electromagnetic waves, the parameters h, k, and w are related to the physics of wave propagation. The parameter h is Planck's constant, while k is the wave number, and w is the angular frequency of the wave. The real parameters are interrelated by the equations ħ = h/2π (where ħ is the reduced Planck's constant), the wave vector K (or wave number k) which is given by k = 2π/λ (where λ is the wavelength), and the angular frequency w which is related to frequency f by w = 2πf. The speed of light c in vacuum is given by c = λf and can also be written as c = w/k, which implies that w = ck. Thus, the angular frequency w is directly proportional to the wave number k for electromagnetic waves propagating in vacuum.