1. The atom vortices are states of atoms which, are characterized by the fact that the angular momentum of the atom along its propagation axis is quantized. The wave-function of an atom vortex is given in cylindrical coordinates as: (p, $, z) = Ale(ap)eitdelkz Where A, a are constants and e = +1, +2, +3, ... is the helicity of the vortex which is associated with its angular momentum along z-axis given by L = he. The vortex carries also a momentum along z-axis given by P = hk. The function Je(ap) is a Bessel function of the first kind. iii) Under what conditions the following wave-function has a definite parity and what is its value? (p, b, z) = Ale(ap)eildelkz + BJm(ap)eimpe-ikz