A mathematical solution of the azimuthal equation  which applies when D is negative, (a) S...

A mathematical solution of the azimuthal equation  which applies when D is negative, (a) Show that this simply cannot meet itself smoothly when it finishes a round trip about the z-axis. The simplest approach is to consider ф = 0 and ф = 2п. (b) If D were 0, equation (7-22) would say simply that the second derivative of Ф(ф) is 0. Argue that this too leads to a physically unacceptable solution, except in the special case of Ф(ф) being constant, which is covered by the mℓ = 0 case of solutions (7-24).