- #1

- 38

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##\left| A \right\rangle = \frac{1}{\sqrt{2}} (\left| \uparrow \right\rangle + \left| \downarrow \right\rangle)##

##\left| B \right\rangle = \frac{1}{\sqrt{2}} (\alpha \left| \uparrow \right\rangle + \beta \left| \downarrow \right\rangle)##

##\left| C \right\rangle = \frac{e^{i \phi}}{\sqrt{2}} (\left| \uparrow \right\rangle + \left| \downarrow \right\rangle)##

(where ##\alpha , \beta \in \mathbb{C}## and ##\phi \in \mathbb{R}##)

Question is, are these states rapresenting the same quantum state?