Interpretation of probability which includes complex number

ChieuVang
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Hi everybody!

I'm trying to find the probability at time t of finding the state pointing in the positive x-direction of an initial system which points in the negative x-direction. I'm not sure if the result is correct, but I get the probability is sin^2(iwt). Can this be understood as the frequency w is a complex number? And what is complex frequency? Or if the frequency is not a complex number, how can I understand the result?

Thanks for your help!

ps: the problem is similar to the example Spin Precession in Sakurai book (page 75), but with complex number in the probability.
 
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