# not separable electron state

Consider electron spin operator. It acts on Hilbert space $$\mathbb{C}^2$$. Next, electron position operator acts on space $$\mathbb{L}^2$$. Can we describe all electron features in one, "joint" Hilbert space? Certainly, both spaces can be combined into tensor product $$\mathbb{C}^2 \otimes \mathbb{L}^2$$, but this looks like composition of the 2 subsystems. If this tensor product is legitimate construction, then the electron states can be divided into separable and entangled. Can particle be entangled with itself?