Invariance Properties of a Proposed Hamiltonian for Bloch Electrons in a Magnetic Field

A matrix equation has previously been proposed for the equation governing the motion of a Bloch electron in a magnetic field. The matrix was obtained by concentrating on irrational fields. The matrix elements vary continuously with the parameters of the problem. It is shown that this Hamiltonian matrix has the normal invariance properties expected from quantum theory. When derived in a Landau base it has an energy spectrum which is invariant with respect to a rotation of the Landau axes about the field. The same matrix equation results for rational and irrational fields if one works in a cylindrical magnetic base.