Difference between an expectation value and an average

In summary, the difference between an expectation value and an average is that the expectation value is the average that you expect to get based on the wave function, while the average is the result of taking multiple measurements of the same quantity. As the number of measurements increases, the average gets closer to the expectation value.
  • #1
Scott4775
9
0
Hi everyone,

What is the difference between an expectation value and an average. I may have this wrong, but is it something along these lines:

You perform a series of measurements on a given observable, such as momentum, and the average value of all these measurements is your expectation value?

I'm sorry if I have this concept totally wrong. I appreciate any help you all may have.

Thanks!
 
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  • #2
The expectation value is the average that you expect to get, calculated from the wave function. As you take more and more measurements of the same quantity, their average tends closer and closer to the expectation value. In the limit as the number of measurements goes to infinity, we expect the measured average to become equal to the expectation value.
 
  • #3
Thank you, that explains it perfectly! :)
 

1. What is an expectation value?

An expectation value, also known as an expected value, is a mathematical concept used to calculate the average value of a random variable based on its probability distribution. It represents the long-term average or the theoretical average of a random variable over an infinite number of trials.

2. What is an average?

An average, also known as a mean, is a measure of central tendency that represents the typical or central value of a set of data. It is calculated by adding all the values in a data set and dividing by the number of values in the set. Unlike an expectation value, an average is based on actual data rather than theoretical probabilities.

3. How are expectation values and averages different?

The main difference between an expectation value and an average is the way they are calculated. An expectation value is based on theoretical probabilities, while an average is based on actual data. Additionally, an expectation value is a long-term average over an infinite number of trials, while an average is a single value calculated from a set of data.

4. When should an expectation value be used instead of an average?

An expectation value should be used when dealing with a random variable that has a probability distribution. This is because an expectation value takes into account the likelihood of different outcomes occurring, whereas an average does not. For example, in gambling, the expected value of a bet takes into account the probability of winning and losing, while the average payout only considers the actual winnings.

5. Can an expectation value and an average be the same?

Yes, an expectation value and an average can be the same in certain situations. This can occur when the probability distribution of a random variable is evenly spread, and there is no variation in the data. In these cases, the theoretical probability and the actual data will yield the same result, resulting in an expectation value and an average that are equal.

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