# Tensor Product Properties

Two spin state are given by $$|\Psi_1\rangle = |\uparrow\rangle$$ and $$|\Psi_2 \rangle = \frac{1}{\sqrt{2}} (|\uparrow\rangle + |\downarrow\rangle)$$.

Which gives the correct tensor product state $$|\Psi_1 \rangle \otimes |\Psi_2\rangle$$?

Note: The notation $$|\uparrow\downarrow\rangle = |\uparrow\rangle \otimes |\downarrow\rangle$$ is a common shorthand for tensor products of spin states.

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