In page 26 of 'Modern Quantum Mechanics (Revised edition)' by J.J. Sakurai, equation (1.4.9), they find the [itex]S_x +[/itex] ket,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mid S_x;+ \rangle = \frac{1}{\sqrt{2}} \mid + \rangle + \frac{1}{\sqrt{2}} e^{i \delta_1} \mid - \rangle[/tex] with [itex]\delta_1[/itex] real. What is this [itex]\delta_1[/itex]?

Furthermore, equation (1.4.8) says,

[tex]| \langle + \mid S_x ; + \rangle | = | \langle - \mid S_x ; + \rangle | = \frac{1}{\sqrt{2}}[/tex]

But if you take equation(1.4.9) and apply [itex]\langle - \mid[/itex] to it from the left, it becomes,

[tex]\langle - \mid S_x ; + \rangle = \frac{1}{\sqrt{2}} e^{i \delta_1}[/tex]

This does not match with equation (1.4.8). There's this extra factor of [itex]e^{i \delta_1}[/itex]

Could someone help me with this? Thanks a lot.

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# Sakurai page 27: What is this 'delta_1'?

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