You should execute this line and the next before you try using this routine.restart;assume(a>0);The following finds the radial wave functions for hydrogen. a is the Bohr radius, r is the radial coordinate, and n and l are the principal and total angular momenta quantum numbers. radial:=proc(n,l) local d;d:=add((-1)^(i-l)*(2*r/n/a)^i/(i-l)!/(i+l+1)!/(n-i-1)!,i=l..n-1)*exp(-r/a/n);simplify(d/sqrt(int(d^2*r^2,r=0..infinity))) end proc:For example, if you want the radial wave function for n = 3 and l = 1, you just plug in these two valuesradial(3,1);Is it normalized? Let's check it.int(radial(3,1)^2*r^2,r=0..infinity);Now let's set up a routine for spherical harmonics. We'll let l be the total angular momentum quantum number and m be the magnetic quantum number, or Lz eigenvalue.spherharm:=proc(l,m) local d,i;d:=sin(theta)^l:for i from -l to m-1 do d:=simplify(diff(d,theta)-cot(theta)*i*d) end do: d*sqrt((2*l+1)*(l-m)!/4/Pi/(l+m)!)/2^l/l!*exp(I*m*phi) end proc:For example, to find the spherical harmonic for l = 7 and m=4, just plug these numbers inspherharm(7,4);Yuck! Is this even normalized properly?assume(phi::real);2*Pi*integrate(abs(spherharm(7,4))^2*sin(theta),theta=0..Pi);The product of these pairs of functions is then the hydrogen wave functions. Maple sometimes has some odd ideas of how to express the answers, howeverradial(5,3)*spherharm(3,1);