- #1
Void123
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Homework Statement
In my textbook, the formula for the expectation value is written as:
[tex] <x> = \int \Psi^{*}\Psi dx [/tex]
Shouldn't there be an [tex] x [/tex] next to [tex]|\Psi|^{2}[/tex] ?
Thanks.
The "x" in the Expectation Value Formula represents the random variable or the quantity we are interested in finding the average value of. It can be any measurable quantity, such as the outcome of a coin toss or the height of a person.
The "x" may be missing in the Expectation Value Formula if it is implied or understood based on the context of the problem. In some cases, the formula may be simplified if the random variable is not explicitly stated, and the "x" is assumed to be present.
To solve for the missing "x" in the Expectation Value Formula, you will need to have information about the other values in the formula, such as the probability of each outcome and the corresponding values of the random variable. Once you have this information, you can plug it into the formula and solve for "x".
Yes, the "x" in the Expectation Value Formula can be a negative value. The random variable can take on any value, positive or negative, and the formula will still be valid. However, it is important to make sure that the values and probabilities used in the formula are appropriate for the context of the problem.
Yes, the Expectation Value Formula is essentially the same as finding the mean or average. It is a mathematical tool used to find the average value of a random variable based on its probability distribution. However, the term "expectation value" is commonly used in the context of probability and statistics.