Interpretation of probability which includes complex number

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SUMMARY

The discussion centers on calculating the probability of a quantum state transitioning from the negative x-direction to the positive x-direction, yielding a result of sin²(iwt). The user inquires about the implications of complex frequency in this context, referencing the Spin Precession example from Sakurai's book. The conversation emphasizes the need to clarify the role of complex numbers in quantum probability calculations.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of complex numbers
  • Familiarity with probability amplitudes
  • Knowledge of Spin Precession as described in Sakurai's "Modern Quantum Mechanics"
NEXT STEPS
  • Research the concept of complex frequency in quantum mechanics
  • Study the derivation of probability amplitudes in quantum systems
  • Examine the Spin Precession example in Sakurai's "Modern Quantum Mechanics" for deeper insights
  • Explore the mathematical implications of sin²(iwt) in quantum state transitions
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Students of quantum mechanics, physicists exploring quantum state transitions, and anyone interested in the mathematical foundations of probability in quantum systems.

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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Maybe you can provide more details about the calculation, so we can help.
 

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