 Single-valued wavefunction

An ordinary scalar wavefunction assigns one complex amplitude to each physical configuration. In polar coordinates without an additional twisted boundary condition, the points $(r,\varphi )$ and $(r,\varphi +2\pi )$ are identical, so the angular factor must be periodic. An angular eigenfunction $e^{im\varphi }$ therefore requires integer $m$. This scalar orbital condition does not rule out half-integer intrinsic spin.