Please help me answer these questions with work. Thank you so much :))))

6) Consider a trial function (x)=Nx(Lx) for 0xL and (x)=0 outside of that interval. (a) Calculate the variational energy W[]=0Ldx(x)(x)0Ldx(x)H^(x) for a particle of mass m in an infinite potential well (particle in a one-dimensional box) of width L. 2 (b) Verify that your result in (a) is consistent with the variational principle, namely W[]E1 where E1=22/2mL2 is the energy of the ground state of the particle in the box. (c) Plot the normalized trial wavefunction (x) and the true ground state eigenfunction 1(x)=(2/L)sin(x/L) on the same graph