Copasetic Flow

After several lectures in other classes where the use of electron diffraction was described in terms of reciprocal spaces, (the Fourier transform of position as opposed to position itself), I finally saw a great explanation of why we work in the reciprocal space to learn about the structure of crystals and other materials in plain position space.  The diagram shown below, (picture 1 on Google+), sums it all up. Put very simply, there's a very clean relationship for how an electron is diffracted based on the electron's momentum wave which is the Fourier reciprocal of the probability vs. position wave in quantum mechanics.  However, to write this relationship down in its cleanest form, you first have to describe the diffracting media in the reciprocal space as well.  Hence, the emphasis on the reciprocal space even though results are often finally translated back to position space for human consumption. The atoms that form the cell structure in crystals are distribute...

This starts a new series of posts that will hopefully inspire discussion among folks taking, teaching, and/or using quantum mechanics.  If you're reading this on Google+, the equations are referenced in the album attached to the post. Did you know that DeBroglie came up with the concept of matter waves considering relativistic invariance? I didn't until quantum I lecture yesterday. Does anyone know how the reasoning went? I can see a way to make sense of it. If you look at energy being equal to, (eq. 1) and think about frequency as the reciprocal variable of time in a Fourier transform, then, if you begin to consider momentum, (the other three components of the energy momentum four vector of special relativity), you soon thereafter could arrive at, (eq. 2) where k is the reciprocal variable of the x, y, and z space coordinates in a Fourier transform. In the same lecture, it was mentioned that the simple form of a sound wave could propagate energy but not mass....