double-slit revisited, motivating why we look now at matter waves...

plane waves

    general form

    relation of k to ω, not generalized to a formula but always has some relation with the wave motion, e.g, ω = kv with v the speed of the plane wave.

    
    group velocity is something I understood much less about.

    From B&S 2.3.2, I see it is bound up in the relationship between k and ω, e.g.,

        ∂²/∂k² ω = β where k = k₀.


the fourier transformation gives a k-space function representation for an x-space wave function at a given time.

for a Gaussian,