Wavefunctions for the quantum regular hexagonal box and microstrip antenna

We calculate the quantum wavefunctions for the thin regular hexagonal box with Dirichlet boundary conditions and for the thin regular hexagonal microstrip antenna with Neumann boundary conditions [1], as was done for the equilateral triangle, square, and circular box and antenna [2]. The hexagonal antenna is relevant to potential Josephson junction devices constructed from a hexagonal cut into the high temperature superconductor,  (Bi 2212). The far-field radiation emission pattern for a few of the antenna wavefunctions will also be presented.