I need to find the coordinate 𝜃 and ϕ values of the quantum state on the bloch sphere $$ \left| \varphi \right>=\frac{1+i}{\sqrt{3}} \left| 0 \right> + {\sqrt{\frac{1}{3}}} \left| 1\right> $$

  • $\begingroup$ Haven't you asked literally the same question before, just with different coefficients? $\endgroup$ – Norbert Schuch Jan 6 at 14:44

You have normalized state $$|\psi\rangle=\alpha|0\rangle + \beta|1\rangle$$

First, write the state as $$|\psi\rangle=\frac{\alpha}{|\alpha|}\left({|\alpha|}|0\rangle + \frac{\beta|\alpha|}{\alpha}|1\rangle\right)$$

The factor $$\frac{\alpha}{|\alpha|}$$ is a global phase and not important. Now you have $$\cos{\frac{\theta}{2}}=|\alpha|$$ which gives the value of $\theta$ and $$\sin{\frac{\theta}{2}}e^{i\phi}=\frac{\beta|\alpha|}{\alpha}$$ which gives the value of $\phi$

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  • $\begingroup$ @Alexey Krugovets $\endgroup$ – Ba. Taj Jan 4 at 11:48
  • $\begingroup$ Okay great job but I have trouble to solve this state. @kludg $\endgroup$ – Ba. Taj Jan 4 at 12:43

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