This is a theoretical physcis question, please answer clearly

The wavefunction of a particle of mass m in the first excited state of a one- dimensional harmonic oscillator with classical frequency w is p(x) = Cxe-12/212 where L = vh/mw. Show that C = v2/(71/413/2) when the wavefunction is correctly normalised. The expectation value of an observable with operator A is DO = $(x) Ao(x) dx Calculate (x), (x2), (p) and (p2) given that the position operator is a and the momentum operator is -inV. You may assume the results for Gaussian inte- grals given below. The uncertainties of the particle's position and momentum are denoted by Ax and Ap and are given by Ax = V(x2) - (x)2, and Ap = V(p2) - (p)2 Show that Ax . Ap = for the above wavefunction