The infinite square box potential. (10 points) - Solve the 2-d Schrdinger energy eigenvalue equation for a mass m in a potential V(x,y)={00x,yaotherwise to show that the normalized energy eigenfunctions are rs(x,y)=a2sin(arx)sin(asy) with energy eigenvalue Er,s=2ma2(r2+s2)22 for r,s=1,2, (Hint: Find the separable solutions (x,y)=X(x)Y(y).) - Show that for each pair (r,s) for r=s then Er,s is degenerate i.e. there is more than one eigenstate with eigenvalue Er,s. - Show that E5,5 occurs with degeneracy 3