1. Find the probability current density for an atom vortex. The wave-function of an atom vortex is given in cylindrical coordinates as: (p, p, z) = Ale(ap)eildeikz Where A, a are constants and f = +1, 12, 13, ... 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