Where psi is orthonormal.jtbell said:[tex]<x^2> = \int {\psi^*(x) x^2 \psi(x)dx}[/tex]
The square of expectation value is a mathematical concept used in statistics and probability theory. It is the square of the mean or average value of a random variable. It represents the expected value of the squared deviations from the mean.
The square of expectation value is calculated by taking the mean or average value of a random variable and then squaring it. This can be represented as (E[X])^2, where E[X] is the expectation value of the random variable X.
The square of expectation value is important in understanding the variability or spread of a random variable. It provides a measure of dispersion from the mean and is used in various statistical models and calculations.
No, the square of expectation value cannot be negative. It is always a positive value because it represents the squared deviations from the mean, which cannot be negative.
The square of expectation value is directly related to the variance of a random variable. In fact, the variance is equal to the square of expectation value minus the expectation value of the squared variable, or Var(X) = E[X^2] - (E[X])^2. This relationship is known as the variance formula.