Infinite well with two regions

[soothsayer]

Imagine an infinite well with two distinct regions in it. In Region A, potential energy is zero, however, Region B has a potential energy level of U₀. A particle with energy E>U₀, is inside the well. In which region is the wavenumber k of the particle larger? A or B?

This was a problem my professor brought up in class, and I was pretty sure the answer was region A, since the wavenumber is proportional to the momentum of the particle, and the momentum is greatest in region A, where there is no potential energy and, therefore, kinetic energy is greater, but my prof. said the answer was B. Perhaps he made a mistake, or maybe I made a mistake (or wrote my notes down wrong) but I don't see how that could be the case, could anyone shed some light on this problem?

 

[stone]

You are correct, since k is proportional to sqrt(E-V), so clearly region A has greater k

 

[soothsayer]

Ohh, ok, just looked over my notes, and the question was not which region k was bigger in, it was which region the wavelength was larger in, which would be B, since wavenumber and wavelength is inversely related. The reason I got confused was because the original question was which region was k larger, but then he changed it. Thanks anyway!