The angular momentum operator L = r x p when written in spherical coordinates contains only the variables theta and phi - not r. Thus, the eigenvectors of the angular moment operators in spherical coordinates may be taken to be functions of theta and phi, i.e., a function on a unit sphere. It is conventional to denote these eigenfunctions as Y_l^m, where L²Y_l^m = hbar² l(l+1) Y_l^m = hbar m L_zY_l^mY_l^m. The Y_l^m or spherical harmonics are orthonormal and complete on the unit sphere. They are used in many science and engineering problems where the functions are defined on a unit sphere (in terms of theta and phi). The condition that the wave function is single valued implies that m is an integer, which in turn impliels that l is an integer for the spherical harmonics.