Short question about probability amplitudes

In summary, the question is asking which form of the probability amplitude (a+bi or a-bi) should be used when given a probability P. However, the concept of probability amplitude can be tricky as different amplitudes can give the same probability, making it difficult to determine the amplitude from the probability alone. This is similar to trying to determine someone's age just from knowing their birthday. An example of this concept can be seen in quantum mechanics with the ψ used in Schrödinger's equations.
  • #1
nomadreid
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When one says the probability amplitude for a quantity when it has probability P, which one does one take, the a+bi or the a-bi?
 
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  • #2
I don't understand your question, perhaps you should try with an example
 
  • #3
nomadreid said:
When one says the probability amplitude for a quantity when it has probability P, which one does one take, the a+bi or the a-bi?

I am not fully familiar with the subject, but it is either |a+ib| or a2 + b2
 
  • #4
nomadreid said:
When one says the probability amplitude for a quantity when it has probability P, which one does one take, the a+bi or the a-bi?

I think the problem is, you are asking the question backward. Many probability amplitudes give the same probability, so you can infer the probability from the amplitude, but not the other way around. Thus your question is like asking how old are all the people who have a May 1 birthday.
 
  • #5
Thanks for the replies.
First, Ken G knew what I was talking about, and his answer makes sense: I gwould guss from his reply that all contexts are "given the probability amplitude A find the probability amplitude B"... ; and none in which you need to find the probability amplitude B given the probability of A. I'll accept that.
Mathman misunderstood my question: I was not asking for the amplitude (which is a2 + b2) but the probability amplitude (which is a+bi such that a2 + b2 = the probability.)
Finally, facenian would like an example of what I am referring to. I am referring to the ψ which you find in quantum mechanics; for example in Schrödinger's equations.
 
  • #6
I think you have it now!
 

FAQ: Short question about probability amplitudes

1. What are probability amplitudes?

Probability amplitudes are mathematical quantities used to describe the probability of a quantum system being in a particular state. They are complex numbers that are squared to give the probability of observing a particular outcome in an experiment.

2. How do probability amplitudes differ from classical probabilities?

In classical probability, the probability of an event is a real number between 0 and 1. In quantum mechanics, probability amplitudes are complex numbers that can have both a magnitude and a phase. The magnitude squared gives the probability, but the phase also plays a crucial role in the interference of quantum systems.

3. Can probability amplitudes be negative?

Yes, probability amplitudes can be negative. This is because they are complex numbers and their squared magnitudes represent probabilities. Negative probability amplitudes can lead to destructive interference and result in a lower probability of observing a particular outcome in a quantum system.

4. How are probability amplitudes calculated?

Probability amplitudes are calculated using mathematical operations, such as matrix multiplication or integration, on the wavefunction of a quantum system. The wavefunction contains information about the possible states of the system, and the probability amplitudes describe the likelihood of observing each state.

5. What is the significance of probability amplitudes in quantum mechanics?

Probability amplitudes are a fundamental concept in quantum mechanics and are key to understanding the behavior of quantum systems. They help explain phenomena such as superposition and entanglement, and their calculation allows us to make predictions about the behavior of quantum particles. They are also used in a variety of applications, including quantum computing and quantum cryptography.

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