|\psi\rangle = e^{i\Phi} \left( \cos\frac{\theta}{2} |0\rangle + \sin\frac{\theta}{2} e^{i\phi} |1\rangle \right) |\psi\rangle = e^{i\Phi} \left( \cos\frac{\theta}{2} |0\rangle + \sin\frac{\theta}{2} e^{i\phi} |1\rangle \right)
