Please explain varience in quantum mechanics...how to solve questions on varience?

Aishwarya pandey

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from it's mean. Variance is the measure of spread of set of numbers from their mean value. In quantum mechanics the basic concept of variance is same as that of in statistics. We have seen that |psi(x,t)|^2 is the probability density of a measurement of a particle's displacement yielding the value x at time t. Now suppose that we made a large number of independent measurements of the displacement on an equally large number of identical quantum systems. Now the mean of all these results is = integral of ( x|psi|^2) Here, is called the expectation value of x. Similarly the expectation value of any function f(x) can be found by putting that function in place of x. In general, the results of the various different measurements of x will be scattered around the expectation value. The degree of scatter is measured by the quantity sigma^2 = integral of [ (x- )^2 |psi|^2 ] = - < x>^2 which is known as the variance of x. and squareroot of this variance is uncertainty in quantum mechanics. So the basic concept is always the same, only the idea of applicability is needed to solve the problems in Quantum mechanics.