N.20 Why Flo­quet the­ory should be called so

At about the same time as Flo­quet, Hill ap­pears to have for­mu­lated sim­i­lar ideas. How­ever, he did not pub­lish them, and the credit of pub­lish­ing a pub­licly scru­ti­niz­able ex­po­sure fairly be­longs to Flo­quet.

Note that there is much more to Flo­quet the­ory than what is dis­cussed here. If you have done a course on dif­fer­en­tial equa­tions, you can see why, since the sim­plest case of pe­ri­odic co­ef­fi­cients is con­stant co­ef­fi­cients. Con­stant co­ef­fi­cient equa­tions may have ex­po­nen­tial so­lu­tions that do not have purely imag­i­nary ar­gu­ments, and they may in­clude al­ge­braic fac­tors if the set of ex­po­nen­tials is not com­plete. The same hap­pens to the vari­able co­ef­fi­cient case, with ad­di­tional pe­ri­odic fac­tors thrown in. But these ad­di­tional so­lu­tions are not rel­e­vant to the dis­cussed pe­ri­odic crys­tals. They can be rel­e­vant to de­scrib­ing sim­ple crys­tal bound­aries, though.