Im doing a problem with a simple model of a carbon nanotube. In this we have an electron which is bound to the surface of a cylinder from which there is a radially outpointing electric field. We choose to put the x-axis along the axis of the cylinder such that the coordinate describing rotation around the cylinder is directly related to its angular momentum. Now I am asked to argue that the expectation value of Lz and Ly are 0 with a physical argument. I am not sure how to approach this. Only thing I can see is that the system is symmetric under rotation around the x-axis, but I don't see where this leads me.