Use Of The Wave Function In The Calculation Of Exp
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Use of The Wave Function In The Calculation of Expectation Values
Any physical property moving in one dimension which does not depend upon time can be calculated from the time-independent (stationary-state) wave function 



According to one of the postulates fo quantum mechanics, as operator for the position co-ordinate x is the multiplier x, therefore the expectation value will be given by

Where p(x) dx is the probability calculated by Born’s postulate.
Similarly, to calculate the expectation value of any other physical quantity (or observable),G, remembering that the operator for G is represented by


Which would be same as the mean value of the results of the repeated experiments for the measurement of G in the state

It may be noted carefully that





p(x) the operator


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