Question

18. The variance of an observable a is defined below. Ta (a2)-(a i) Find an expression for the variance of the momentum (operator defined below) for a one-dimensional particle in a box of length b. dx i) Find an expression for the variance of the position (operator defined below) for a one-dimensional particle in a box of length b.

Answer 1

Variance for part a) = ($\hat{p}$^2 )-($\hat{p}$)^2

                            = (ih)^2* d^2/dx^2 -(- ih *d/dx)^2

Variance for part b) = ($\hat{x}$^2) -($\hat{x}$)^2

                            = x^2 -(x)^2