The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l = 1 dispersion relation, and a previously published l = 2 dispersion relation is shown to be partially incorrect. The Hermite–Krichever Ansatz, which expresses Lamé equation solut...

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the " rest of the universe " contained in his 1972 book on statistical mechanics. T...

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the " rest of the universe " contained in his 1972 book on statistical mechanics. T...

The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l = 1 dispersion relation, and a previously published l = 2 dispersion relation is shown to be partly incorrect. The Hermite–Krichever Ansatz, which expresses Lamé equation solution...

The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l = 1 dispersion relation, and a previously published l = 2 dispersion relation is shown to be partially incorrect. The Hermite–Krichever Ansatz, which expresses Lamé equation solut...

We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a band gap or split the degeneracy into a pair of linear degeneracies that are continuable to Dirac points. A degeneracy of this type occurs between the second and...