Probability of an observable

In summary, the probability of an observable is a measure of the likelihood of a certain outcome in a given situation or experiment. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Theoretical probability is based on mathematical calculations while experimental probability is based on actual data. The probability of an observable can be influenced by various factors and understanding it is important for making informed decisions and predictions in various fields.
  • #1
radinic
1
0
Hey,

How would you compute the probability of measuring a specific value of an observable (resp. range for continuous variables), given a wavefunction with an eigenbasis that is different from the one associated with the observable?

An example: Let's consider my wave function is a superposition of energy-eigenfunctions, how would I get the probability of finding the momentum in a range [a,b]?

Best
 
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  • #2
1) Obtain the momentum representation wave function.

2) Integrate its absolute square over the appropriate interval.
 

1. What is the definition of probability of an observable?

The probability of an observable is a measure of the likelihood that a particular outcome or event will occur in a given situation or experiment.

2. How is the probability of an observable calculated?

The probability of an observable is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

3. What is the difference between theoretical and experimental probability of an observable?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely, while experimental probability is based on actual data collected from experiments or observations.

4. How can the probability of an observable be influenced?

The probability of an observable can be influenced by various factors such as sample size, experimental design, and external variables. It can also be influenced by the laws of probability, which dictate the likelihood of certain outcomes based on the available information.

5. What is the importance of understanding probability of an observable?

Understanding probability of an observable is crucial in making informed decisions and predictions in various fields such as economics, finance, and science. It also allows us to assess risks and make sound judgments based on the available data.

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