Consider a particle moving in a scalar potentialV$(vec(r))=V_z(x)+V_y(y)+(V{)}_z(z)$

a$)$Show that the Hamiltonian can be written as:

$(H)=(H{)}_x+(H{)}_y+(H{)}_n,$ where $(H{)}_z=\frac{(p{)}_z^2}{2m}+V_z(x)($similarly for $(H{)}_y$ and $((H{)}_z$