  Rotationally invariant combinations of the Brillouin zone-center Bloch
functions are used as basis function to express in cylindrical coordinates the
valence-band and Kane envelope-function Hamiltonians for wurtzite and
zinc-blende semiconductor heterostructures. For cylindrically symmetric
systems, this basis allows to treat the envelope functions as eigenstates of
the operator of projection of total angular momentum on the symmetry axis, with
the operator's eigenvalue conventionally entering the Hamiltonians as a
parameter. Complementing the Hamiltonians with boundary conditions for the
envelope functions on the symmetry axis, we present for the first time a
complete formalism for efficient modeling and description of multiband electron
states in low-dimensional semiconductor structures with cylindrical symmetry.
To demonstrate the potency of the cylindrical symmetry approximation and
establish a criterion of its applicability for actual structures, we map the
ground and several excited valence-band states in an isolated wurtzite GaN
quantum wire of a hexagonal cross-section to the states in an equivalent
quantum wire of a circular cross-section.
