I think we have the answer here:
http://rsta.royalsocietypublishing.org/content/368/1914/927.full#sec-7
The first momentum, calculated through the de Broglie relation, represents the canonical momentum. While the second one represents the kinetic momentum. I'm not entirely clear with the...
That is a good point. But I still remain confused: if nothing happens to the momentum of the photon inside the medium, how is it that the wavelength changes? Or, since the wavelength is changing, doesn't the momentum have to necessarily change?
@sophiecentaur
I don't see why not? In fact see: http://en.wikipedia.org/wiki/Photon#Physical_properties
(And that's a featured article, so I guess we that's a safe reference there)
Quantum Computers are not believed to be able to solve NP-Complete problems. But if quantum mechanics were non-linear, then it's a different story as shown here:
http://arxiv.org/abs/quant-ph/9801041
Probably adds to the evidence the QM is fundamentally linear.
A photon goes from vacuum into a medium. This causes its momentum to reduce. Hence by the de Broglie formula, its wavelength should increase.
But, since the refractive index of the medium is greater than 1, and
n_2/n_1 = \lambda_1 / \lambda_2 , and hence, its wavelength should decrease...