Interpretation of probability which includes complex number

In summary, the conversation discusses finding the probability at time t of a system initially pointing in the negative x-direction and later pointing in the positive x-direction. The result is found to be sin^2(iwt), which raises questions about the frequency w being a complex number and the concept of complex frequency. The problem is similar to an example in Sakurai's book (page 75) but with a complex number in the probability. More details about the calculation are requested for further assistance.
  • #1
ChieuVang
1
0
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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  • #2
Maybe you can provide more details about the calculation, so we can help.
 

FAQ: Interpretation of probability which includes complex number

What is probability?

Probability is the measure of how likely an event is to occur. It is typically expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

How does complex numbers relate to probability?

In probability, complex numbers are used to represent the amplitude and phase of a wave function. This is commonly seen in the field of quantum mechanics, where complex numbers are used to calculate the probability of an outcome for a particular quantum system.

What is the difference between real and complex probability?

Real probability deals with events that have a single outcome, while complex probability deals with events that have multiple outcomes. In real probability, the probabilities of all outcomes must add up to 1, while in complex probability, the square of the amplitude of all outcomes must add up to 1.

How is probability interpreted in the context of complex numbers?

In the context of complex numbers, probability is interpreted as the square of the amplitude of a particular outcome. This means that the larger the amplitude, the more likely the outcome is to occur.

What are some applications of complex numbers in probability?

Complex numbers are used in various fields, including physics, engineering, and finance, to model and analyze complex systems. In probability, they are used to calculate the likelihood of an event occurring and to understand the behavior of complex systems with multiple outcomes.

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