Angular frequency of a matter patter

[redtree]

By the de Broglie relations: E = $$\hbar * \omega$$

Is the angular frequency ($$\omega$$) in this equation an average or is it a constant? In other words, does the angular frequency (or the wavenumber, k) for a matter particle change, for instance, in differing gravitational fields, such as we see for a photon with gravitational redshift?

 

[redtree]

I can restate the question in a related way.

Assume a spin-1/2 particle is described by a probability amplitude function ($$\Psi$$) with angular frequency ($$\omega$$) or wavenumber (k). The probability amplitude distribution for that particle exists within a volume of space-time. Assume that within that volume of space-time, there is an electromagnetic field that varies significantly in strength over that volume. How does that varying electromagnetic field affect the wavenumber/angular frequency of the particle's probability amplitude distribution?

 

[ZapperZ]

Er... I have almost no clue on what you're getting at here.

Let's look at a less "exotic" example, shall we? Something that every single physics undergraduate does - tunneling through a square potential barrier. Look at the wave vector as it goes through the various regions. Does it change?

Zz.